I support all of these recommendations. I also enjoy Tekken Tag Tournament 2, but I don't really play PS3 games any more.
To elaborate on Scaff's recommendation of Metal Gear Solid, there are seven games in the series available on PS3 and as the storyline is continuous from the very first game (made in 1987) to now I recommend you play them all.
There's Metal Gear Solid, the PS1 game, available on PSN. Then there are the HD remakes of Metal Gear Solid 2, 3 and Peace Walker on PSN separately or you can buy all three on a disc which is probably cheaper. Metal Gear Solid 4 is only available on disc though. As a great little bonus, the HD remake of Metal Gear Solid 3 also contains the ports of Metal Gear and Metal Gear 2.
If you play through them all (either in chronological order (MGS3, Peace Walker, MG, MG2, MGS, MGS2, MGS4) or release order) the saga will probably blow your mind. Or it'll drive you insane, one or the other, it's all good fun at the end of the day. Oh and only Peace Walker has multiplayer features. MGS4 used to have an entire multiplayer game, Metal Gear Online, but it was shut down and then patched out of the game. Peace Walker feels very similar to that though (but obviously with inferior graphics as it's a PSP port). That reminds me; if graphics are important to you then you might want to take a look at the games before you buy them, only MGS4 has up to date graphics and even they haven't aged brilliantly!
