What makes a good video game great?

A while ago I was reading a thread asking individuals what games they had last played multiple times.

Unfortunately, I actually have a hard time coming up with more than a couple, even though I'm sure I must have played games all the way through when I had more time (id est, in college).

The only two I could think of were Uncharted: Drake's Fortune and Metal Gear Solid 4: Guns of the Patriots.

I played Uncharted, from beginning to end, three times. The third time was because trophy support had been added in, and I wanted the trophies for what I'd already been able to accomplish before.

Metal Gear Solid 4 I did an initial play, doing whatever I felt like (and eventually what the game finally beat into me as how I shoiuld play if I wanted to finish it), and one more with zero kills.

I believe I played through Final Fantasy VII twice, as I first purchased and played the PC version, and then the Playstation version. While I think I finished the PC version, I can't recall for certain (but I'm almost positive I did).

I started a second playthrough of Final Fantasy X-2, but I only got a little way in before I got wrapped up with other things.

I've tried to play FF8 and FF9 a number of times, but never stuck with it long enough, which could also be said for a handful of other games.

Ultimately, it was the story that really drove me on in both Uncharted and MGS4; I played them and didn't get sick of them.

Now there's other games that I've picked back up, after 'beating' them, such as FFXII, Katamari Damacy and We Love Katamari (although not so much the latter), LittleBigPlanet, and way back when, Super Mario World and Mario 64. (And I'm very tempted to play through the first Shadow Hearts again, because I remember loving it when I first played it, because of the story and gameplay.)

Ultimately, then, it is the story that really makes a game worth it to me, in that I want to go through the game again.

I was lent Bioshock, and I think that may take another spot in this short list (although whether it's the 360 or PS3 version that takes it, depends upon time).

My only hope is that Uncharted 2 and Bioshock 2, not to mention some game among all those other games that will be out between now and the former, will be a part of this list as well ...