I've had no problem plugging in my Sega Master System or Nintendo and playing a few games. Most are unbeatable. I also have a rather extensive jrpg collection that I will filter through now and then (especially Chrono Trigger and FF7).
I haven't plugged in my old atari in forever, and don't know if the controllers still work, so that's up in the air. But I have no problem playing roms of the games I had on it, like Populous, warlords, HitchHiker'sGuidettG, and SimCity. If I could find my old pong system, I'd so plug it in.
If you're referring to more recent 'old' games, sure. I can go back and play through them with no issue. In fact, I still go and buy older games. Sometimes I am surprised by things, like camera angles (recently bought DMC1). Nothing that wont stop me from playing it.
Personally, I believe graphics have spoiled people. Gives them an excuse to not play good olde classics. And it's a pathetic excuse in my opinion, as there are some great games in history that, regardless of graphics, are a blast to play.