So I got a Samsung Epic and I'm working on my app library.
Either games or not-games, doesn't matter. What things are neat?
"SNesoid" and "GameBoid" are emulators with free versions (no savestates, but with the normal battery saves). There's also a ROM finding app called "Emulator ROMs" that is shockingly easy, for downloading roms of the games you already own (naturally). They use multitouch and put the controls on the screen itself, which is a lot easier than it sounds to control; you won't be playing Super Metroid very well, but Final Fantasy and Advance Wars and stuff are fine. Okay, you CAN play Super Metroid, but I only got out of the exploding space colony with like ten seconds left, so it's tricky. They also work with slide-out keyboards of course.
Geocaching and geohashing are, of course, quite cool. I enjoy c:geo for my geocaching needs, and there's an actual "Geohash" app as well.
"3D Compass" is awesome if you have an AR-capable phone. It displays the camera image, with a compass overlaid, basically just like if you were holding one out in front of you (great for getting exact bearings to visible landmarks). Map in the corner, all that good stuff.
"SoundHound" uses the mic to record whatever song you are listening to, and identifies it after about twenty seconds. Just press the big shiny button when you want to know what that song on the radio or the grocery store speakers is. Seems to deal with noise pretty well. Mostly limited to popular stuff, but hey, if you hear it played in public and don't already know what it is, it's probably in its library.
"DroidTropes" STAY AWAY, YOU DON'T NEED TVTROPES ON YOUR PHONE
"File Expert": Lets you run http and ftp servers ON YOUR PHONE. Public-facing IP, for me at least. How fucking awesome is that.
All these are free, and they haven't broken my phone yet...but of course, use at your own risk.