Ok, there's really no order because I don't even wanna start to think about which I prefer over others even if theres obviously preferences.
1 : Resident Evil 4
This is the single-player game which I re-played the most. I played through it 3 times on gamecube, did it again on PS2 + the extra contents and then again on the HD remake on Xbox 360. It is by far the best game of the series, gameplay is imo perfect (yeah, better than the run and gun of RE6, because it removes so much of the tension), it is quite challenging, which is always a plus for me, has a good length (15 hours or so for a first run is pretty damn solid for this genre). Action-packed, but not too much since the horror feeling was still there, even after playing it several times. Such a classic!
2 : Metroid Prime
A shooter, an adventure or a platforming game? Metroid Prime does it all with a perfect pacing. I've done it 3 times, which put it just behind RE4 for the number of playthrough. It also feels like an open-world game, since theres different way to progress and you can always go back to previous places to search new upgrades and such. The soundtrack is also pretty damn solid for a non-rpg game.
3 : Starcraft : Broodwar
Ok, i'll say it now, i've never played the campaign. For me, this game is all about the multiplayer competitive scene. It is by far the most complicated online game and it requires a shit ton of skills and knowledge to be decent. Being a competitive person by nature, it's no surprise that I got hooked from 1999 to this day (well, I switched to Starcraft 2 last year). There's literaly tournaments of high quality to watch every single weeks, if that's your thing.
4 : Gears of War
I didn't bought the last of the series (Judgement), but I've played a tons of the first 3 and what got me addicted to this game was the unique 3rd person/cover system gameplay. I know theres a lot of 3rd person shooters now, but none does it as perfectly as GoW. The campaigns are pretty solid, although cliche, for a shooters, but it's all about the multiplayer again. Although i'm now a retired Gears players, I had good times with it! Having a team is a must, though, since it can be very frustrating to play with randoms teams since it requires quite a lot of teamplay for the genre.
5 : Lost Odyssey
Creator of the Final Fantasy series and Nobuo Uematsu on the soundtrack, this couldnt went wrong, right? Well, that's what I told myself and I wasn't disappointed. I know for a lot of people this was just another JRPGs, but for me it was an instant-classic. There was nothing really new, but being kinda conservative in my taste of games, I had no problem with it. Good story, awesome soundtrack, good variety of ennemies, beautiful and plenty of CGs, that's enough for me. I even cried a tiny bit at some point (ending of 1st CD or beginning of the 2nd, not sure anymore), which is a sign that the story is good.
6 : Final Fantasy IX
FFIX is the only other game which made my eyes wet (only at the ending this time, though. spoiler : theater scene, zidane show up, dagger go ape-shit and run to see him, awww). Beautiful soundtrack, environements and story did it for me. Special mention to : FF4, FF6, FF7 and FF10, which I all liked a lot, too, but i want to make place for others series.
7 : Mass Effect Trilogy
I'm normaly not into sci-fi futuristic RPGs, I prefer the fantasy-medieval theme, but for some reason I loved this trilogy so much. Maybe it's because it's a blend of shooters and rpgs, well, it's probably that when I think about it. The immersion is flawless, we need more of this genre.
8 : Elder Scrolls : 4/5
I still can't tell if I prefer Oblivion or Skyrim, both have aspect that are better than the others. I played about 150 hours on both and just like Mass Effect, I think the strong point of these games is the immersion. 5 hours of gametime in this feels like 2 at most.
9 : Golden Sun 2
This is probably only because of the nostalgia since I played this as a kid, but fuck I had a good times with this game. Theres also probably the fact that I was playing it along side of my 2 cousins at the time, so we hyped ourselve to death everytime we saw each others, which was often back then. I liked the uses of the magic (psynergy I think it was called) on the worldmap/dungeons, it was original). Overall a solid standard JRPG that you can play on the go since it's on GBA.
10 : Tales of Symphonia
Sheena, mostly. I liked the little skits, gameplay which was new to me at the time and every little details in this game.