Here are the applications that I utilize most often on my Blackberry Storm:
UberTwitter: An awesome app for mobile Twitter.
Pandora: mobile Pandora is music to my ears.
Gmail: The Gmail app for the Blackberry Storm has the best scrolling of any app on the phone…it’s even better than the apps by RIM.
Slacker: Another web radio app, similar to Pandora.
Facebook: It’s mostly useful for reading status updates. Mobile Facebook via the Storm’s browser works well too.
Google Maps: Great for when you get lost or need directions. Uses the Storm’s GPS when it’s active.
Flickr: Take photos with your phone and upload them to your Flickr account.
YouTube: Watch your favorite YouTube videos on your phone.
BuzzMe: Runs in the background. Allows for your phone to both vibrate and ring during incoming calls.