For me, it has to be divided into categories and a few winners picked.
Zelda: Ocarina of Time on the N64 was one of the best games I've ever played - to this day - in terms of overall story, writing, puzzling, the world it immersed you into, the steadily improving boss battles etc. Just an all round fantastic and immersive gaming experience with very few flaws.
Kung Fu Chaos on Xbox may not have been the all time greatest game, but the sheer number of hours I clocked up playing on multiplayer with friends justify it as quite possibly the most enjoyable multiplayer experience in any game that I've ever played. Very, very, addictive. Easily my favourite beat 'em up.
GTA: Vice City probably remains my highest game time on any game. The possibilities in replaying the game in the sandbox world meant I was just never bored, even if it was going on rampages three years later.
Halo (1 and 2) is another game that was just absolutely sublime in terms of adversaries, universe, graphics, game play and - for me at least - the introduction of a genuinely enjoyable co-operative play. Legendary on the Library, slogging away to complete the level for three/four hours, remained fun throughout in a way that few games do after even a quarter of that time on a single play through.
Honourable mention must go to Battlefield (Bad Company 1,2 and BF3) due to the sheer number of hours I spent on - and enjoyment I got from - online multiplayer; throughout gaming in halls at the very beginning of the PS3's lifespan to still hammering BF3 now just as BF4's been launched. The more I consider this, the more I think I should go out and buy BF4 at the earliest possible opportunity.
I'm not sure how I managed to forget it, but Pokemon (Yellow and Silver specifically) has to be included. I started with the franchise on Yellow (I was a kid on holiday in Spain and it had just been launched, which is where I bought it) and just loved absolutely everything about it as a kid at that age. Also racked up a hell of a lot of time completing, restarting, training and completing Silver.