It's impossible for me to list them in order as I don't have a favourite game, but here are my 10 favourite games in no particular order:

Final Fantasy IX
Tony Hawk's Pro Skater 3
Resident Evil 4
Phantasy Star Online
Super Smash Bros. Melee
Legend of Zelda: A Link to the Past
Mario Kart: Double Dash
Halo: Combat Evolved (PC Version)
Tibia (MMORPG)
Breath of Fire III

Honourable mention: Grandia I and II, Suikoden II (This would be in my top 10 definately, but I've only briefly played it. Enough to know I love it though) Time Splitters 2, Kingdom Hearts.