MixZing: Better than the stock music app solely because of its ability to automatically download album art.
Ringdroid: Excellent ringtone creator. Use any song on your phone!!
Shazam: Some pretty impressive tech. Recognizes seemingly most songs playing on your radio or in a store, etc. Listens for a few seconds, then gives you artist and song title. I love it.
PdaNet: Tether your phone without rooting and without paying. If you have unlimited data plan, you should have no worries here. Simple and amazing. Must own for you non-rooters.
Laputa: So many amazing free ebooks to download. Some comments in the app store claim that other apps have a better selection, so I tried them. My testimony: This is the only app that let me download every Harry Potter book. Yeah, I have every Harry Potter book on my phone. FOR FREE. Just do it.
Google Sky: Watch as your phone magically transforms into a window into space. This app uses augmented reality better than any app I've tried, and it will impress everyone around you. Point your phone to the sky and move it around. It will tell you what constellations you're pointing at in real time, along with planets and the moon and its phase. Simply incredible.
Astro: If you're going to torrent applications to save yourself some dough, you're going to need this or something like it. It's basically like running "Start Search" on your mobile device, giving you access to all of your files.
Shopper: This may not be the best app for the job, I've yet to test. But it's worked almost flawlessly for me so far. Scan bar codes, check for better prices online. See which stores are ripping you off. Pretty cool stuff, man.
Advanced Task Killer: If used properly, this will keep your phone smooth and save some juice. Just don't kill any tasks that you'll find yourself reopening again soon. That's been rumored to suck more power than save.
That's all I got. I'm new.