i feel overwhelmed....... this device is amazing!
That feeling will take a long, long time to wear off. I'll try to avoid repeats, but with so many apps, I'm too lazy to recheck everyone's post.
Get yourself Astro File Manager, it lets you move and rename and so on and so on. Just get it.
I'd recommend the Amazon non-MP3 app.
If you want to do a lot of music and video sideloading without plugging in your usb, AndFTP is the best ftp client, lets you use your home wifi network. I think Swiftp or SwiFTP or Swift FTP is an ftp server for your phone, but I found it's easier to run the server on your computer and the client on your phone.
Get Gmote. You can use that same wifi network to control a media player on your computer. Yes, you just got a free, huge touchscreen media remote for your computer.
Locale is fun to mess around with, but depending on how you spend your day, it might not be that useful. If you spend a lot of time turning your phone's silent/vibrate/ring depending on meetings or classes, get it.
Android Agenda Widget is the best widget I've found for syncing your google calendar to a good looking, customizeable widget.
Apps Organizer is good for organizing folders of your ever growing and changing apps library.
Backgrounds is good for finding backgrounds that don't involve T&A, and it can even autochange your background based on a series of things you've favorited.
I found GDocs good for a simple, lightweight notepad that will sync with Google Documents. It can't handle opening other formats though, but more often I just want to write down something I thought of, or quickly refer to something I thought of while at my computer.
Google Listen is good for podcasts, but it doesn't really do as much in the cloud as you'd expect from a Google App these days. And it doesn't handle all of my podcasting needs- For example, I also use Stitcher. I also don't really recommend Police Scanner. If you can find the internet stream addresses online for your town's police band, there are internet stream apps that are free. You're paying money for someone to assemble that list for you, he doesn't maintain the streams in any fashion. I think I use DroidLive or Droid Live as my shoutcast-type streaming app, and I have a couple NYPD and FDNY bands favorited in that.
Meridian is the music player I use for downloaded stuff, they all have their pros and cons, but Meridian is the one I found that (when I checked) had a widget like the default Music app. The others didn't really have home screen widgets, and I've found that essential.
Mobile Defense is good if you lose your phone, but it also won't save your battery from dying once its lost.
NetCounter is good for getting a gauge on how much your using your data plan, which on Verizon is 5 gigs per month.
OpenTable is cool, but personally not enough restaurants support it. Other good restaurant apps are Places, Where, and Aloqa.
Pandora, Last.fm, iheartradio and Slacker are all fairly essential, though Pandora probably most of all unless you're already a heavy last.fm user.
If you have a laptop and often find yourself in places without free wifi, and you also have netcounter installed and running, get Pdanet. But I'd avoid a lot of video downloading/streaming, that can eat up 5 gigs fast.
Photoshop has Photoshop.com Mobile, which does pretty much what you need it to. Cropping and the like, plus some minor effects.
SaveMMS lets you save MMS attachments to your SD card.
Twidroid Pro is what I use for twitter, but there are some pretty good free ones, like Swift. (Not the FTP Swift app I was talking about.) I've heard good things about Babbler for Facebook, but I don't like Facebook enough to warrant getting the paid version, and Babbler Lite didn't impress me.
SleepTimer is a great app, since very, very few media players come with a sleep timer function. All SleepTimer really does is force kill a preset-by-you process, so it will probably even work for something like Pandora. In other words, you don't need to wait for the app to officially support whatever music you listen to. It also has a really cool function I've discovered. You're listening to music to fall asleep, and you set the timer to 20 minutes. Twenty minutes go by and you haven't really fallen asleep, and all of a sudden your music shuts off. Now you have to roll over, grab your phone, open your eyes, play something again, reset the sleep timer.. And afterwards you're even more awake than you were when the music shut off. What SleepTimer will do is play a quick chime when you have one minute left on your sleep. You then reach over and shake the phone a little, and bam, another 20 minutes of sleep. That's it. Chime, shake, it chimes again at you to let you know you added more sleep. Really, really cool.
Now, there's also White Noise and Sleepy Time. These aren't sleep timers for your music, they play nature sounds and fans and the like. Like the white noise machines you see in Skymall. They have their own built in sleep timers.
Movies, by Flixster is also a good app. And I think Fandango came out with their own app too. Showtimes, trailers, even buying tickets.