I don't know if I could ever do a top five list for all games played ever; I'd have to go by console, but here goes anyway:
1. Sonic 2. The first game was great, but Sonic really found his stride with the second game. The sense of speed is far more satisfying, the music is punchier, level design is tighter, and the diffiuclty was ramped up just enough to be challenging compared to the first. Some people have mixed feelings about Tails, but there was sort of a fun quasi-co-op quality where someone could hop on the second controller and help lift you up somewhere.
2. Riven: The Sequel to Myst. The first Myst was the epitome of PC game design: it was almost zen-like with its simple interface, rich and detailed world, and low system requirements. That said, it didn't age all that well in the following years. I'm never one to bash graphics, but when the gameplay is as straightforward as point-and-click, it's not unreasonable to want a little more eye candy, and Riven looks just as beautiful today as it did back then. The addition of people might have been a shark-jumping moment, but encounters were so few and far between, it dispelled the loneliness of the first without being overbearing.
3. Star Ocean: Till The End of Time. I was too time-invested in Final Fantasy's games to give Star Ocean: The Second Story a glance when it came out, and I really regret it. Till The End of Time was one I didn't have much faith in as I'd been burned by a few other RPGs prior and was sort of beginning to lose my taste for them, but Star Ocean changed my mind and then some. It's one of those games to which I've attributed a lost weekend, the sort of marathon gameplay experience wherein the only reason I stop playing was the revelation that I needed sleep.
4. Final Fantasy VIII. This one had to grow on me. I'd played a demo and was rather put off by the 'follow-the-leader' party system (though it's probably more realistic than the 'body jumping' in VII). The magic system intrigued me, as did the slightly more unconventional story, I bought the game shortly after the demo but didn't actually put it in as by then I was growing tired of the RPG genre (that and people wouldn't shut up about the stupid card game which was anything but fun). Five years later, long after X came out, I decided to give it a go and somehow absolutely fell in love with it. I actually prefer this one to VII.
5. Zone of the Enders: The Fist of Mars. A turn-based strategy game that includes elements of arcade shooters, this game enthralled me by virtue of its story as much as its unique gameplay. It's also the only time I think I've ever laughed at that 'amnesia' joke... and I was on a crowded plane when I let the laugh out.
Even still, I'm cringing at all the other good games I've left out, I don't think even a top 10 would suffice.
Worst games is a bit easier:
5. Sonic Adventure 2
4. Unlimited Saga
3. Haven: Call of the King
2. Fighting Force 2
1. Supercar Street Challenge
Okay, that actually wasn't easier. Maybe I need higher standards.
EDIT: added qualifying remarks to top five list.