I have a SGS2 myself, loving it! How long does your battery usually last? I find myself having to charge nearly every day but a friend with a very similar usage pattern only has to charge every other day. His phone is newer than mine but we run the same software versions :-/

Here's the stuff I use:

  - DrumSound app for those times you need a quick drumsound! http://trommelyd.no/ 
  - JuiceDefender (free at the moment), seems to help a lot. 
  - Twitter/Facebook/Google+, hoping the average person will move to Google+ as I find it much nicer.
  - Connectbot IRSSI for SSH (and irssi)
  - AlarmDroid, for much better alarms/countdowns/timers.
  - Spotify for genious easy music playing (requires premium)
  - 3G Watchdog to keep track of my BW usage. I have a 600MB quota I'm never close to.
  - RealCalc for a better calculator on the go.
  - Dropbox to easily access things
  - Notifo for awesome irssi highlight notifications as well as pushing the current page I'm visiting from chrome to the phone (say I'm looking at a recipe and I'm going to the store)
  - SSHdroid (not used often) to ssh into the phone.
  - ElectroDroid for amazingly useful calculators, resources and pinout info.
  - Hacker News and Reddit is fun
  - Google Docs
  - Various games (Angry Birds, Dragon Fly!, Fruit Ninja, X Construct and the FPse emulator)
  - Hacker's Keyboard, full-sized keyboard which is nice for SSH
  - SoundHound for recognizing songs
  - EverNote (not used much) for keeping notes
  - Astrid Tasks for keeping tasklists
  - A flashlight app for turning the lights on/off.
  - Epicurious for food 
  - DuckDuckGo app for super easy access to information

As well as a bunch of Norwegian-only apps (Package tracking, norwegian equivalent of Epicurious, City Bike info, Bus info,Yellow pages)

Wow, I really use a ton of apps.