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 Art is timeless, graphics become outdated.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.