It is a matter of opinion. In my opinion, the original Jak game was the best. But MOST people prefer the second one. There wasn't enough Ico in the other ones.
First one was very simmiliar to Crash Bandicoot series, Jak II is something more innovative - open city, guns, dark eco e.t.c., but yeah, it's matter of opinion. I think that all Jak's (except X) are great. I'd take everything from Naughty Dog blindfolded, they never relased any crap.
TIMESPLITTERS FUTURE PERFECT...MY PERSONAL FAVORITE resident evil 4 the incredible hulk shadow of the colosus psi ops devil may cry gta san andreas final fantasy XII timesplitters future perfect is an awesome first person shooter, with an amazing mapmaker, tons of weapons, lots of characters, you can customize almost every aspect of the game you are about to play, and if you are into glitching there are lots of glitches (not because it is poorly coded or something it has just been out for a while so alot of glitches have been found.)
I got resident evil 4 limited edition in a metal box, for 2 pound. Grate game for the price, pure classic
I'll list at least one of each genre for you Devil may Cry I,II,III Star Ocean 2 - Was really good Okami - Epic. Definetly a must try. I myself have played it countless times Final Fantasy X Ico - Classic PS2 game Valkyrie Profile:Silmeria Timesplitters Future Perfect Ace Combat:Squadron Leader Atelier Iris 3: Grand Phantasm - The battle system is really fun Tekken (3,4,5) God of War I, II **I don't recommend FFXII, while holding the FF name, the game is too long, and the trials and obstacles are too long. Although fighting may have seemed fun, it got tiring. I prefer to be pressing some buttons during battles. Although, the choice is really up to you.**