Deposit a check:
Chase (Stock Quote: JPM) and PayPal (owned by Ebay(Stock Quote: EBAY)) stand out among the bank-owned apps because of one unique feature, which I'm sure won't be unique for long. They offer remote check deposit. Snap a picture of your signed check, verify the details and confirm. Check deposited! This pretty much eliminates the last need to stop by the bank.
Chase Mobile available on iOS, Android (free): Check out the Chase app here.
PayPal Mobile available on Android, iOS and Blackberry (free): Check out the PayPal app here.