Stumblers have been demanding this for long and finally the engineers at StumbleUpon have delivered it. You can now stumble through your phone using official iPhone and Android apps. The Android app will require you to have either Eclair [2.1] or Froyo [2.2]
All you have to do is download the free app, login with your credentials and all your settings will be imported.
From Official Blog
You can stumble all topics at once, just like on your computer, or stumble in a particular topic. We’ve also made it easy to stumble in some of the most mobile-friendly channels we have: Photos, News, Flickr and YouTube. In addition, you can share your favorite sites directly to other Stumblers and via Facebook, Twitter or email.