Keep in mind my perspective as you read this. These are not (necessarily) the best video games of each year, but rather the best *thinking games* for digital platforms. (I'll throw in my opinion about the most important / influential / best video games from time to time, but they'll be limited to honorable mentions.)
2000 - The Sims
I'm never quite sure how to categorize The Sims. It's always labeled as a "strategy game" in video game market research reports, but it doesn't really have winners or losers. I've always counted Dungeons & Dragons as a thinking game, so I think I'm supposed to count The Sims too. Meanwhile, there can be no doubt that this was an incredibly well executed and wildly popular game.
Honorable mentions: Diablo II, Counter-Strike.
What an amazing year. Diablo II is still the best action RPG of all-time, and was my own guilty pleasure game for many years. And Counter-Strike (which is technically a user-generated mod of Half-Life) showed people how poplar an online multi-player shooter could be (a genre that still dominates the industry to this day).
2001 - Party Poker
I could just as easily have given the nod to Poker Stars, which was a bit better polished at the time and is bigger today (plus Paradise Poker pre-dates both of them), but it was really Party Poker and it's aggressive marketing that launched the online poker boom. No one in the video game industry seems to talk much about online poker, but I'm not sure why not. They're games for digital platforms that make tons and tons of money, right? They also fundamentally changed the landscape when it comes to thinking games and thinking gamers. Suddenly it was possible to directly apply your gamer skills to making money.
The Magic: the Gathering Pro Tour was a nice dream, but the truth was that only a couple dozen guys could make enough money to live on and nobody was getting rich. Kai might have had a $100,000 year once, but the typical good years were in the $50,000 range with $20,000 very much in play. Don't get me wrong, that's a hell of a lot better than flipping burgers (even before you count the fun of traveling the world and hanging out with cool people) and it's a lot of money when you're college-aged; but it's not really a career. Most of the really great players eventually find something more lucrative to spend our time on. Meanwhile it's really tough to stay on top of the game unless you're devoting all of your time to it, so the Pro Tour winds up with a steady stream of hungry 20-somethings rising up and dominating for a couple of years before they grow up and move on.
Anyway, the poker boom provided a way to pursue the whole "gaming is way more fun than getting a real job" thing while having significantly more earning potential. The World Poker Tour launched in 2002 and things really heated up when Chris Moneymaker won the World Series of Poker in 2003. Not only did he provide an "anybody can win" story that the media adored, but he also won his entry fee in a PokerStars satellite tournament, thus attracting a lot of "dead money" to online poker as his "turned $39 into $2.5 million" story was told over and over again.
A funny thing happened to the Pro Tour with lots of its players turning to poker. Very few of them stopped playing Magic. Magic became the game that they play for fun after grinding out a living playing poker. Just because there aren't as many opportunities to win money playing Magic as there are in poker, doesn't mean it's not the more fun game. Dave Williams is probably the most visible example of this — he's been a very visible poker celebrity ever since finishing 2nd in the WSOP in 2004, but he's also continued playing Magic the whole time ranging from late-night drafts in Vegas with other Magic/poker cross-overs to a steady string of money finishes on the Pro Tour to tweeting while in Europe about the crappy WiFi that won't allow him to play Magic Online. My favorite Magic/poker cross-over story, however, is Gabriel Nassif. Nassif has managed to stay one of the best couple of players on Magic's Pro Tour for the entire decade while also making the transition from "omg this is a lot of money for a 16-year old" to "my poker ev is better, but I still love Magic."
There were some other decent thinking games in 2001 — Kohan was an intriguing take on how to do a real-time strategy game that didn't require great twitch skills, and Advance Wars really moved the tactics genre forward — but from my seat 2001 was the year that online poker changed everything.
2002 - Magic Online
Magic players used to stop playing once it became inconvenient to find opponents to play against. Around the time they graduated college, or got married, or had their first kid it became hard to make time to head down to the friendly local game store and Magic became a victim of these lifestyle changes. Ever since Magic Online came out, however, that just doesn't happen any more. Now there's always a new draft about to fire and the 10pm draft after your kid goes to sleep can be followed by the midnight "bad idea" draft. The product definitely has its flaws and it's not hard to imagine ways it could be a lot better, but if you compare life as a Magic player nowadays to life as a Magic player before 2002, things are just more awesome because Magic Online exists.
This isn't a Magic decade in review, however, so I want to talk about Magic Online in the context of other video games. I'm pretty sure it's the #2 turn-based strategy franchise of all time. Civilization has made more money, but I don't think anything else has. I'm still bound by an NDA that prevents me from discussing the details, but it's not hard to triangulate off of publicly available numbers and project a lifetime revenue above $100 million. That's not in the same league as Grand Theft Auto or World of Warcraft, but it's still quite a respectable number, especially for a PC-only title. I wonder sometimes whether the mainstream video game world realizes how much money Magic Online has actually made.
In addition to proving that a turn-based strategy game can make real money, MTGO also proved that the digital object sales model can work. This may not sound like such a big deal nowadays with everybody's facebook wall littered with posts from social games that make their money that way, but back in 2002 it was still very much an open question. Many folks gathered at industry conferences and discussed the reasons why the so-called "Korean model" couldn't work in the States. Well it did work. Magic Online obviously had all the advantages of its relationship with Magic (built-in / captive audience, known great game-play, etc.), and it's never done a particularly good job recruiting new players into Magic (every MTGO player, to a first approximation, starts out as a paper Magic player), but within the context of Thinking Gamer awards there's nothing wrong with that. Everyone who likes strategy games will try Magic at some point and most will love it.
2003 - Galactic Civilizations
Kind of a weak year. I almost gave the nod to Madden '04 because they re-did the engine behind their franchise mode, which is essentially a stand-alone football simulation game with a fair amount of depth and re-playability. (Madden itself is the kind of game that used to make me jealous of people with high dexterity scores, but as I've grown to embrace who I am as a gamer I go straight to the franchise mode, sim all the games, and play what amounts to a gigantic, well-flavored spreadsheet game.) Meanwhile, the most innovative game released in 2003 was almost certainly Defense of the Ancients (DotA) - the mod of Warcraft III that has become so wildly popular that multiple AAA-sized projects are now coming out which attempt to recapture that gameplay within a "real" game. DotA is too much of a dexterity game to get the nod from me, though, so I'm calling out a solid new franchise developed by Stardock. Stardock has also turned into a nice home for various strategy games and genres that the big publishers don't seem to care about and their
Impulse digital distribution system has much of the same functionality as Valve's much more heralded Steam.
2004 - Oasis
Like some of my
board game choices, this one may be biased by the fact that I currently work for Mind Control Software. That said, I was not around when they developed this game and it did win several indie game of the year type awards. It's essentially a civilization-style experience boiled down into about 5-10 minutes of turn-based strategy goodness.
Honorable mention: Others seem to like the Total War series more than me, but from what I can tell 2004's Rome: Total War was the best of the series. Oh by the way, this was also the year Blizzard unleashed World of Warcraft on an unsuspecting world.
2005 - Civilization IV
A really nice step forward for this venerable franchise. Civ III (which came out in 2001) was quite bloated, with an accumulation of new mechanics and new ideas really weighing down the game. With Civ IV they finally started cutting stuff away, eliminating the extraneous baggage so that the underlying awesome gameplay could shine through. I had thought that Civ II (which I spent many an all-nighter playing while in college in the early 90's) might have been the peak, but Civ IV was genuinely better. I also enjoyed Civ IV: Colonization, which uses the Civ IV engine to play out a New World scenario where you work for one of the European powers as they seek to colonize America and you win by seceding and then winning the revolutionary war. It's less open-ended, but the base game can sometimes take 10-20 hours to play so it's nice to have a more compact experience.
Honorable mention: Guitar Hero launched rhythm games as a mainstream phenomena and the first truly new genre added to the video game landscape in about a decade.
2006 - Galactic Civilizations II, I guess
Hopefully somebody will post a comment with a better suggestion as I don't think Gal Civ is worthy of winning two different years, but turn-based strategy remains a niche in the video game world and there have been some dry years ...
Honorable mention: Wii Sports. The innovations continue over on the more mainstream side of the industry with the launch of the Wii and the introduction of motion controls to console gaming.
2007 - Desktop Tower Defense
I know this wasn't the first tower defense game, but it was the first one that hooked me. It also gets credit from me for bringing
Kongregate to my attention as a website full of free games worthy of checking out semi-regularly. I will always remember the first time I played it when I had the flash of insight "OH! I build a MAZE!" and to this day I don't particularly care for the fixed-path tower defense games. The challenge of figuring out how to build the maze is the best part of the genre, in my opinion, and DTD is well balanced, well executed, and damn close to the platonic ideal of this genre.
Honorable mention: Speaking of new platforms that make significant amounts of new content available, Xbox Live Arcade started coming into its own in 2007, with digital versions of a couple of tabletop classics (Settlers of Catan and Carcasonne) among the highlights.
2008 - Braid
Playing Braid remains one of the most jaw-droppingly, mind-blowingly awesome experiences I have ever had with a video game. The time-manipulation mechanics are brilliant and the level-design is incredibly clever. Multiple times I would find myself just staring at the screen thinking, shaking my head in amazement, and knowing that the answer was there if only I was smart enough to find it. It is crystal clear to me that this was a labor of love for Jonathan Blow and the extra years he spent tightening and polishing it really show.
2nd place: Civilization Revolution. Civ Rev is by far the best game in the almost 20-year history of this franchise and it would have won most of the years in this decade. It's essentially a slimmed down version of Civ IV designed specifically for console and handheld gaming, but that's "slimmed down" in the sense of "I am so much healthier now that I've lost 100 pounds." The challenge of porting the core experience onto devices that don't have mouse/keyboard really inspired the designers and developers to ask themselves what actually mattered and the resulting game has all the strategic depth and strategic fun of a 20-hour long Civilization session boiled down into a game that can be finished in just 2-4 hours. It's the only game on Xbox where I have fully 1000 gamerscore.
Honorable mention: If you play (tabletop) Dunegons & Dragons, you really should check out
D&D Insider. The Character Builder is exactly the tool you've always been hoping for (with every rule from every book and every issue of Dungeon and Dragon magazine coded into it) and that plus the Compendium make prep time a pleasure instead of a chore. I can no longer imagine building a character any other way.
2009 - Drop7
If you're a thinking gamer and you have an iPhone then one of two things is happening right now. Either you're smiling and nodding knowingly or you're going to trust me and go straight to the app store and buy this game. It's a fairly simple game ("Tetris meets Sudoku" is the best description of it that I've heard), and the presentation is pretty sparse, but the strategy involved is remarkably deep. Hardcore mode is the best way to play as things get interesting right away and there's just the right amount of randomness so that it's replayable, and you can catch a lucky break, but you are also convinced that skillful play is what really matters. My only tiny complaint is that I really wish they would track a running average of your last 20 games. It tracks high scores and average score (and if you put in your facebook info then it will let you compare high scores with friends), but with 500+ games under my belt it's hard to move either of those numbers now.

Other 2009 finalists: Fieldrunners is a nice "build your own maze" tower defense game for iPhone. Duels of the Planeswalkers is a really nice way to play Magic against an AI, especially if you're still learning (or re-learning) the game. (It's currently only on Xbox Live Arcade, but is supposed to come out for PC and PSN in 2010). Plants versus Zombies is a bit too easy for my tastes, but it's turn-based strategy done with all the quality and polish that you can count on from PopCap.
Honorable mention: I also quite enjoyed Dragon Age, and definitely recommend it if you're looking for a single-player RPG experience.
Decade in summary
My top 5 are Magic Online, PokerStars, Braid, Drop7, and Civilization Revolution. They're so diverse that I'm not sure I know how to rank them relative to one another. Online poker has had by far the most financial success of these five, and has changed the lives of many thinking gamers by providing them with a source of income. However, at the end of the day poker isn't as much fun as the other games on this list so it can't win. Braid is probably too small to be game of the decade. It's an awesome experience, but once you've solved it, you've solved it and you probably aren't going back to re-play it. Drop7 seems like it might be a bit too small (and a bit too unpolished) to win as well. Civ Rev didn't win it's year, but I do find it interesting that I'm still playing Civ Rev a year later whereas I'm not playing Braid any more — it does have the virtue of being quite re-playable. I even downloaded Civ Rev for my iPhone so I could work my way through some of the scenarios that I hadn't gotten to (something I don't recommend unless you already know how to play Civ because the interface is about two notches worse on an iPhone).
All of which leaves me with Magic Online. I'd feel better if it was a better polished product, or a product that I could recommend with a clean conscience to folks that don't already know how to play Magic, but even with those flaws it's still an awesome addition to the life of any Magic player. And Magic is the best thinking game of all time.
Looking forward
Well that's my take on the decade in video games. Things were a little dry for us thinking gamers in the middle of the last decade (and the early years were saved only by MTGO and poker), but now there are a bunch of new digital distribution platforms available where publishers and/or game designers can profitably target a niche audience like us. Of the 10 games I called out from 2007 - 2009, only one of them (Civ Rev) can be purchased at a brick and mortar store. Things are looking up and I'm excited to see what the 20-10's have to bring!