well. I really can't pick between Star Wars Battlefront and Timesplitters 2 for my favourite.

I have recently gone back to playing Timesplitters 2 again. I just love its wackiness. It has unlockable cheats throughout, but they're not normal. Silly hats anyone? how about paintball versus fat cardboard cutouts with big hands and big heads. I don't know any other game where you can be fighting so many different characters (126 of them). Its an adventure through time from 1853 to 2401. Personally I like 1920's Chicago, taking down Big Tony (with TNT and dual wielded tommy guns).
The music is the best I know of in a game and i never block it out with my own music. in fact, I have the whole Timesplitters 2 album on my walkman.
The amount of depth to this game is stunning. There are 3 game cartridges hidden in the story levels, games within a game. there are awards in the arcade mode for doing various things (brain surgeon, most cowardly, hypochondriac, lemming award, backpedaller...etc). There are challenges like breaking all the Notre Dame windows as an undead priest with a grenade launcher.
But perhaps the best thing is it is hard. Not just hard, but really frickin hard. I had completed most of the game before I had completed the first story mission on hard mode. Some maps it is frustratingly hard, but there is always a way to do it without getting killed, there is never someone just around the corner who will always hit you.
Don't get me started on the multiplayer part.

This is my other favourite game, also on PS2, also a FPS. Except this is a class based game where you take over command posts to gain control of the battlefield. It also doesn't take itself seriously, which is good. Most battles have an array of vehicles which you can pilot (or steal). This leads to a vast amount of things which you can do in each battle.
For example, at Geonosis you can:
- take an AT-TE and blast your way about.
- take an LAAT and destroy the techno-union ships.
- Be a soldier and go forward to take either the East or West Bunkers, or both, or the Spire.
- Stay and defend the main base from droidekas.
- Sit back and snipe
- Take a jet trooper and try climb the spire
- Try steal a spider walker
And that is just a few options if you're playing as the Republic.
Most battles are either 200 or 250 troops, with 10% of that number fighting at any one time. I love the replayability of Battlefront,
every battle is different.
Also, the game doesn't care about realism in most places, which leads to some pretty funny things. For instance I use the sniper as a front line soldier because the gun is a fast firing with a two shot kill, also the sniper can launch orbital strikes (haha why?). The Empire's shock trooper has a missile launcher that I like to use as a sniper rifle.
There's something really satisfying about picking off an enemy sniper with a missile, or shooting a guy about 5m away and watching the body fly away. Another thing really good about Battlefront. The ragdoll movements from a grenade (or missile, mortar, mine, turret, etc) are as good as in N. And that's true with grenade jumping too.
Also, it is a very hard game sometimes (Empire at kashyyyk: islands is near impossible in one player). I like to lose a battle every now and then, because it makes it even more of an achievement if i can conquer the galaxy without losing a battle.

Awesome game. And even better that my brother has done a full modification of the game to our likings (units, technologies, terrain, cities, leaders, civilisations, rules, resources, buildings, art). Complete with his wacky humour.
eg "The wanker Australians have taken Ha Noi. Make them pay!!"
Recently we have found that he can turn an existing single player game into a multiplayer. Effectively he can join in my own game, taking over an existing civilisation.
Honourable mentions to:
Crash Bandicoot
Jak 2
Age of Empires 2: The Conquerors Expansion