One of the first console game I ever bought, loved it from day one, still love it today.
That game turned out to be TimeSplitters. At first I was skeptical (first game for Free Radical. Who?), but after booting it up for the first time I knew that i was in for a treat in this game.
OK, so the single-player is lacking to say the least, but this isn't a game to be played alone. The story missions have the very basic objective of picking something up and taking it to a certain point, for EVERY mission. However, once you've got the tedious 'Story' mode out of the way, there is the much more enjoyable Challenge mode, which involves crazy objectives, such as 'Kill 100 ducks in the fastest time possible', or 'Smack as many heads off with your fists as you can'. Genius, but rock solid all the way through.
But, let's be honest, you wouldn't buy this game to play the single-player mode, because the multi-player part of the game is UNBELIEVABLE. Great characters, excellent levels, fast-paced gameplay and just all out fun contribute to making this one of the best multiplayer games on the PS2, to this day (Except TS2, obviously).
Also, the mapmaker is easy to use and adds hours of extra gameplay to this already fantastic game.
All in all, an excellent buy, whether or not you own the slightly superior TS2.