Lots of the 2600 library is still eminently playable today. Games don't have to be "modernish" to hold up well. A good game is a good game from any period. Someone mentioned chess. Sure not a video game but the thread title didn't specify video games so technically an excellent answer to the question.
I said "modernness."
To an eye looking back, some of these games can feel very modern in setting, style, and set-up. For instance, one of the DnD games on the Intellivision is a first-person dungeon crawler with surprisingly modern elements, all from an era where 3-D movement didn't really exist.
The most important part, I think, is control. If the game controls in a way that a modern gamer will instantly recognize and be able to adapt to, it feels as though it could be a modern game--that's timeless, that "ages" well because, in a large part, it may get older, but it doesn't actually
age.
I mentioned Galaga because it still feels fresh and modern--shmups prior to Galaga feel dated and archaic. Space Invaders is slow and clunky. Galaxian is just slow. But Galaga nailed the speed of attacks, the intensity of the gameplay, and the smooth, solid controls.