1. Super Mario Bros./Duck Hunt - The first game I ever remember playing and, being extremely young at the time, can't say I was any good at either of them. But I enjoyed them both and it planted the seeds that would eventually turn me into the gamer I am today.
2. Pokemon Blue - First game I really got into, having already seen the show and gotten the cards, it was the first game I actively asked for from my parents. Until then, I had always just played whatever games my parents just happen to buy, with little input from me or from my brother. It's also the first game I ever finished and to this day I still remember that, for some reason, my final team included a Lv. 100 Victreebel.
3. The Legend of Zelda: Wind Waker - Probably the first game I fell in love with. My parents, up until that point, had forbidden me from ever playing any of the Zelda games due to some religious over-protection. I missed the first game, A Link to the Past, Ocarina, etc. It wasn't until after getting a Game Cube, a friend of my recommended the game to me. I think I rented it from Blockbuster, because I spent a few days while home from school sick playing through it. It was a magical experience and, to this day, is still my favorite Zelda game of all time.
4. Halo: Combat Evolved - The game that turned me into a hardcore gamer. Until I reached that point, while I liked playing video games, they were not a major form of entertainment for me and I made no effort to keep up with the news of the industry or about new releases. But after just one local multiplayer match in Halo, my world was completely changed. Very shortly afterwards I traded in my Gamecube stuff and bough an XBOX along with a copy of Halo. I also became more interested in gaming as a whole and started reading magazines and articles online to keep up with the new releases. This game also cemented my love of the FPS genre.
5. Okami - Hands down, Okami was a revelation. To this day, this is my favorite game of all time, a masterpiece that has yet to be topped by any other game I have ever played before. The combination of art style, music, gameplay and a story soaking in Japanese mythology left my blown away when I first played it and I have made sure to always have a copy in my possession even if circumstances force me to sell my collection.
6. Castlevania: Dawn of Sorrow - The game that turned me on to going back and playing retro games. Now, by itself, it wasn't retro at the time. When I had played it, however, I had never played a single Castlevania game before it and once I completed it during college, it awoke the desire to go back and play the older Castlevania games, going all the way back to the original NES trilogy. That opened me up to playing other old games I missed out and turned me on to so many classics I missed. Also the game that made me love the Castlevania series and Metroidvania-style games.
7. Chrono Trigger - This established my love of the SNES and is my favorite RPG of all time. After being turned on to retro games by Castlevania, I picked up the DS copy of Chrono Trigger due to the overwhelming positive reputation it had and it absolutely lived up to the hype. For me, it established that 16-bit is probably the era that is going to hold up the longest. The beautiful sprite work of Chrono is still a sight to behold to this day and even now I wish more indies attempted more 16-bit style games rather than just 8-bit.
8. Shovel Knight - The game that introduced me to the indie scene. I had heard about it some time before, but didn't buy it until a physical copy came out on the 3DS. I picked it up and fell in love with it. It introduced me to the indie scene, which has probably become my favorite part of gaming right now. A fantastic alternative to the samey AAA titles pumped out each year by the big publishers. Including Shovel Knight, some of my favorite games from the past decade have been from the indie scene.
9. Dark Souls - I was intimidated the hell by the game when it came out and I shied away from it for some time even though I really liked the looks of the game. I was given a free download code for the first game during one summer home from college and spent much of that time pushing myself through the game. I fell in love with the game, and with Souls-like games in general and it made me realize that difficulty didn't necessarily have to be something to avoided.
10. Telltale's The Walking Dead - I was once a fan of The Walking Dead and since this was the first big game with the license, I picked it up without second thoughts. This game helped create my appreciation of 'walking simulators', as I really enjoyed the more deep plot even though it didn't have the most in-depth gameplay elements. But that was ok, and it has helped me appreciate other games in the same vein, like Gone Home, Tacoma and The Town of Light.