Well, the thing about old games is that they have one thing new games almost inherently lack: Pick-up-and-play designs. It's near impossible to play something like, say, GTA4 for an hour or two, put it away for several weeks, then pick it up again and feel as if you're right in the thick of it. There was plot that you've probably forgotten about; you might not even know what you have to do next! What about your friends and dates, remember how far you were with them or where they live? (actually it's been a while so they might have had locations shown on the map but you get the point). What about certain games where you can't even save for about a half hour? You're required to dedicate that time to the game, and if you might not have it or you don't feel like playing that long, you are SOL. Now look at something like Sonic or Super Mario or Mega Man. You can jump in and instantly you are playing the game. Not wandering around looking for a mission or re-reading plot from last time you played. In fact, what was amazing about those games is that often levels were full of hidden caches and secrets that you might randomly come across one game, and maybe find a different one next time. You'd often have new things to discover. In this I found Sonic an exceptional example; several levels had many different ways to get to the end, and so often were there challenges along the way and hidden areas that you could search for. You could play the same level 10 times and do it different each time. This keeps the game feeling fresh and exciting no matter how many times you play it.
Of all the games that came out in the past few years, the only big seller that included this was Portal. The compartmentalized style of puzzles made it easy for you to come back to it, and it didn't take but a moment to remind you that you are most likely being tested by some giant insane computer. And even after the game was done they took it upon themselves to offer you some new, incredibly difficult challenges that made you look at the levels in a different way.
In any case, the reason I find myself going back to my classics is the simple fact that I know, as soon as I turn that game on, I can be having fun.