Go Launcher EX - If you would like a more customizable home screen other than the stock one, I suggest Go Launcher EX. Then, download the Black Chrome Go Launcher Theme, or any other that you would like. That's just what I like. If you don't like that one, another good option would be ADW Launcher.
Facebook, Twitter, other social media - Totally your preference. Download what you would like. Just make sure you change your settings so they send updates every 15 minutes and not constant push. That will drain your battery like crazy.
ASTRO File Manager - Good file manager, if you don't like it there are plenty other free ones on the market to choose from.
Wheres My Droid - In case you ever lose your phone, this is a good app to locate it.
YoubTue - Another personal preference app. Download at your convenience.
The Weather Channel - This is the weather app I use, but you may prefer a different one. Try some out and choose the one you like the most.
Go Switch Widget - Put it on your homescreen. You can control when you want 4g/3g, wifi, airplane mode, battery life, etc.
Handscent SMS - Great messaging application. Use this is Go SMS. Both are great. Personal preference.
Tiny Flashlight + LED - Best flashlight app. Tons of settings.
Words with Friends, Angry Birds - Games; download whatever you would like.