Here's a pretty good list to get you started. Just about all of them are free or have a free version out there.
Music:
Zedge (free ringtones/wallpapers),
Soundhound (recognize any song),
DoubleTwist (converts itunes playlist into android format),
Music Junk (not on market, but can download after Google search of Music Junk. It's like Napster for Androids).
Useful apps:
Advanced Task Killer (conserves battery life if you use proper settings),
Astro File Manager (can move, rename, or delete any file on you device),
Bump (to share apps, photos, contact information with other android phones that download Bump),
Dropbox (to easily transfer files from computer to your phone)
Firefox (fastest web browser on any android phone)
Fancy Widget (HTC like clock and weather widget)
Gmote (control your itunes on your computer with your phone) *great for parties*
Google Translate (translates from english to spanish or any other language)
Movies by Flixter (movie times, reviews, etc for nearby theaters)
MicDroid (voice changer to sound like Lil Wayne)
Tango (allows video chat over the 3G network)
Widget Locker (customize your lock screen so the unlock looks like an iphone, HTC, android, etc)
Games:
Live Hold'Em - Poker game where you play against other people, not against a computer
Angry Birds - One of the best games EVER
Gun Brothers - Fun as can be shoot-em-up game that you can literally play forever
Hex Defense - Tower defense game that is addicting once you get the hang of it.
NOVA - excellent first person shooter very similar to HALO
Words Free - it's basically Scrabble for android phones and iphones
aTilt 3D - rolling a marble through a maze by tilting the phone. Very Fun
There are so many more, but there's quite a few here to keep you more than busy for a long time.
-Anonymous