Me personally the longevity of the game. If you can boot the game up after a while, and it's still fun. That's a good game. IMO at least
It's all just in how solid it is. Sometimes it helps to completely reinvent things (like RE4) but most of the time, just having really fun gameplay can be all it needs. A great story is also a great, but less common, way. No one remembers Doom for the story, you know. But something like Mass Effect has a good balance of fun gameplay and great story.
I'd attribute it to two things:
- Gameplay mechanics: It's actually FUN to play. (ex. Mega Man games...simple mechanics, but rock solid, responsive, and never gets old)
- Art Design: Notice how I didn't say "graphics" here? Art is timeless, graphics become outdated. (ex. 16-bit Sonic games...sure, they were big shots in the graphics department back then, but the sprite work is still attractive to this day)
...To me, graphics, story, character development are all nice things to have, but aren't necessary in a "classic". I'm debating whether music should be one of the requirements, since I can't recall a great game going without a great soundtrack.