It hurts not including great franchises like Civilization, but cutting off after the PS1 era means many of my favorite iterations from the old franchises are not included. Here I go:
10. Chrono Trigger
Chrono Trigger, the game that matches FF6 as my favorite JRPG of all time. The music, gameplay, graphics/art, story, and characters all amount to nothing short of perfection. Chrono Cross is included in the series as well, which was a decent game.
9. Starcraft
The greatest RTS ever solos its way onto the top 10. Not much else needs to be said about it - to this day, I still play the game occasionally.
8. Mario Kart
Super Mario Kart was my favorite racer up until Mario Kart Wii. That's saying something! The game surprised me, as it kind of came out of nowhere (I didn't know what the hell a go-kart was). The music is still the best in the series, and the game remains fun to play to this day. The 2 player GP is huge for people like me, who always have a sibling in the room (we would otherwise take turns). Mario Kart 64 wasn't quite as good, but it was still a solid game, and its battle mode remains the best in the series.
7. Counter-Strike
It's only a single game, sure, but the hours I spent on it were ridiculous. This is the game (or mod) that started it all. There isn't an FPS I've played nearly as extensively, not even close. Hell, I joined a tournament for this game, which remains the only time in my life I'd done something of the sort. Note that the vote is for Counter-Strike, not Half-Life, so count it accordingly (not a fan of HL so don't contribute to its votes, lol).
6. Quake
My favorite was the first in the series, though the fact it had 3 games in the PS1 era helps its position. Quake was the first game I'd actively find mods for (I was 9-10 yrs old when it came), so that gave it a ton of replayability, especially since we had 3 computers set up for LAN goodness in the house. Team Fortress was born on Quake, and I had plenty of fun with it (more so than Valve's version). The most addictive mod by far was AirQuake, the best flying game (or mod) I've ever played. Man, thinking about it makes me want to force my friends to set it up and play some rounds...
5. Super Mario Bros.
I was never a fan of the first game, but Super Mario Bros. 2, 3, World, and 64 are easily among my favorite platformers.
4. Final Fantasy
My favorite JRPG series overall. FFVI is my favorite, with FFX not far behind. FFIV and the PS1 RPG's were great games, though I was initially disappointed with FF7 after playing it on PC. Still, the games were consistently very high quality, with FFVI in particular boosting the series above Mario.
3. Diablo
Diablo was awesome, as it was one of my first online games. Although the hackers (town killing!) were annoying, it was a great introduction to online gaming for me. Diablo II released before PS2, so I believe it counts - that game is simply awesome. It provided entertainment for years! In fact, I only stopped playing it after WoW pretty much replaced it for me, which is amazing considering I was also playing the (ridiculously time consuming) Everquest. I revisit the game every now and then for fun.
2. Heroes of Might & Magic
Heroes II and III were freggin amazing. Seriously, these games are not given nearly enough recognition - I'll be disappointed if I'm the only one who votes for this awesome franchise! They've also aged so well, with its great music and charming 2D sprites. I plan on setting up some Heroes III games with friends soon. If you don't know what this franchise is, do yourself a favor and look into it, now!
1. The Legend of Zelda
Not much to say here - both NES titles rocked, and A Link to the Past and Ocarina of Time are among my all time favorites. Ocarina in particular is tied with my all time favorite games ever (along with FF6, CT, CS, etc). Having 4 games this strong cements the series into the #1 spot.
