I've been playing around with game console emulators for Android on my HTC Inspire a lot lately. Spending more time gaming than I should be, but whatever. There will be time to do work and improve my programming later. Anyways, there's a bunch of different open source game console emulators that have been ported to Android and packaged into paid apps, but many of those have been kicked off the Android Market and you can get them for free, for now.
Gensoid - This Sega Genesis emulator is the main one I've been spending (too much) time with. I recently completed Sonic the Hedgehog 2 for the millionth time. Sonic 2 was the very first game I ever owned, the Genesis was my first console and first device I could game on since we couldn't afford a PC. Because of the ring-collection mechanism that keep you from dying instantly, Sonic is much more playable without the precise controls of a hardware keyboard than something like Mario is. The on-screen virtual keyboard works fine for games where you don't get insta-killed.
Snesoid - Snesoid is a Super Nintendo emulator, and although I was a Genesis-kid I'm keeping this installed. Trying to play Super Mario without a real keyboard is tricky, so I limit my time with Snesoid to playing at a table with my bluetooth keyboard. Since it's so easy to die in SMB you really need the better controls. Or maybe I just suck, since I grew up a Sega fanboy and only played Mario on a cousin's Gameboy.
Gameboid - Speaking of the Gameboy, you can get an emulator for that too.
In fact, you should probably just go ahead and download all the Yongzh emulators at SlideMe. They're free for now and who knows for how long, because Google removed the paid versions from the Android Market, possibly due to pressure from companies like Sony/Sega/Nintendo.
The coolest emulator to show off is the PSX one. Running Playstation games on your phone is nifty, even though actually playing some of them is a bit wonky, even with a keyboard to give you more buttons. Maybe it's easier if you've gone and gotten your PS3 controller working with Android, but even that is limited in compatability and the analog sticks apparently don't work yet. Still, a cool thing to demonstrate to friends.
The best things to play with the Playstation emulator are probably relatively easy to control games like simple racing games. Sled Storm is a game my family and I spent a lot of hours playing back in the day, and it's fun to relive some of that by playing it on my phone. It's also a neat thing to showoff to the less technical people I know.
The Playstation emulator needs a bios file to work, and obviously you'll need to get roms to play games with the emulators. I won't link to the bios file needed to run PSX4Droid, nor will I link to any sites with game roms. Just trying to avoid getting in trouble. Use Google if you need to. Stuff is out there.