I used Advanced Task Killer for awhile (the first 4 weeks) then removed it last week.
I have noticed no issues regarding battery life. Funny how the consensus on if it's necessary goes back and forth, but for now I am living without it with no problems.
As for must have apps, Shazam (or Soundhound), MP3 Downloader, Slacker Radio, Camera 360, Flixster, Layar, DirecTV app (YMMV), Weatherbug Elite, Dolphin HD or Skyfire browser, Setting Profiles. I would include Fring...but now without Skype it's useless.
And some other keyboard (like Swype or SlideIT...haven't personally tried out Swype...still waiting for the non-beta release)