Sly 2: Band of Thieves
I accredit this game with cementing my interest in the hobby. It was one of my first PlayStation 2 games and from the time I popped the disc in, I was enthralled. It remains one of my favourite games of all time, on part due to the nostalgia factor admittedly, but it's still a great adventure. Climbing around Paris, picking guards' pockets and feeling like the world is mine to conquer with my thiefiness...ahhhhhhh, good times. Sly 2 also made me a lasting Sucker Punch fan.
The Elder Scrolls IV: Oblivion
My dream RPG, in a nutshell. I must've put well over 300 hours into the game by now, including about 140 on my beloved Khajiit, though I'll let you in on a little secret: I've never made a mage character, or even bothered with magic aside from the occasional heal spell. The atmosphere of this game is so much better than Skyrim's generic "epic fantasy" crap. Oblivion is full of flaws to be sure, but they're all very forgivable in the face of the grand adventure and hours of fun it's provided me with.
Final Fantasy VII
There simply had to be a Final Fantasy game on this list. I'm a massive fan of the turn-based combat in the series and the overall structure the games possess, aside from how they tend to take a very long time to really get going. I was debating which one to choose for awhile. X-2 was actually my first FF and I considered putting it on here for that reason, but while I did enjoy it a great deal, it's not...Final Fantasy-like enough to deserve such a position. VII was the first FF I finished proper and I loved just about every moment of it. The materia system is also my favourite, as it's easy for newcomers to grasp but you can spend a lot of time and effort strategically improving your characters with it. There is definitely good reason that a lot of people obsess over this game.
BioShock
Oh, BioShock. How can I even begin to explain my love for this game? Well it's pretty much the only first-person shooter I like. And I like it a lot. It also significantly contributes to the argument that video games can certainly be art. BioShock 2 was a decent sequel, but there's just no comparing it to the original. I believe I finished BioShock three times in a handful of months after I first got it and never got bored.
Kingdom Hearts II
While the first game has the better story in my opinion, KHII was a major improvement in most other areas. Boy, was I obsessed with this series for awhile. I've fallen out of touch with it in recent years due to the unfathomable amount of spin-offs they've released on platforms I don't own, but Kingdom Hearts II in particular still holds a very special place in my heart. I remember buying it before I'd finished the first game, rushing to do so and then beginning my Kingdom Hearts journey anew. I have some pretty big gripes with the series, but overall it's just a blast to play and the game's final bosses in particular are magnificent.