just some off the top of my head on my phone ....
Lookout..... mobile security (scans every download)... but most importantly allows you to locate or completely LOCK a lost phone if needed
Shazam
Astro ..... file manager
PdaNet..... tethering app
Ringroid.... easily make ringtons from MP3 right on the phone
Barcode Scanner
Sports Tap.... sports scoreboard of sorts
Google Voice .... must have this for free text messaging and will transcribe voicemails and send as texts, among other things
Weatherbug is the best weather app Ive seen on there so far
Pandora Radio..... streams music from personalized selections
Camera360........ absolute best camera program Ive found
as far as games everyone will have their favorites..... I personally like Bonsai Blast and What The Doodle
if you really want to change things up a bit then you can try some different launchers:
I recommend getting Home Switcher which allows you to easily switch your launchers...... most popular launchers seem to be ADW.Launcher and Launcher Pro...... Ive tried them both and still prefer the Sense....... but you can really customize your screens with different launchers where Sense is what it is
some other handy apps that I use regularly are:
Wifi Analyzer..... shows all available signals and their strength etc
Gmote..... allows you to use your phone as a remote for your PC (can control media player/keyboard/mouse)
GPS Test..... scans for Satelite signals etc...... also has handy little compass
GPS Status....... similar to above
as far as task killers go...... generally they are totally unnecessary on an android phone......because of the way android handles applications...... however they do come in handy for those pesky apps that never want to close on their own
there are various tips on improving battery life...... task killers dont fall into any of them..... there are things you can do though..... I personally use my phone quite a bit with different apps and browsing etc...... I still get anywhere from 24-36 hours before I even consider a charge.... I can go 2 days with moderate use.....
try turning off the mobile broadband when not in use....... you dont need this for the phone to function as a Phone......also the GPS is a big drain........ also not needed on when not in use....... haptic feedback drains alot........ theres tons of other things as well....... just have to go through and turn off the things that you dont really need running