Chase Bank came out with a mobile app QuickDeposit feature (take a picture to deposit a check) last year, I am not sure if they were the first but they have certainly started a mobile banking revolution. I have always thought this feature as one of the finest examples in creating the perfect mobile experience. Looks like a number of folks like Charles Schwab, State Farm Bank and Paypal are also joining the party.
Here is a quick round-up of each bank's mobile deposit limits:
Chase: QuickDeposit (Android / iPhone) $1000/Day, $3000/Month (Link)
Schwab: Mobile Deposit (Android / iPhone) (Link)
State Farm Bank: MyTime Deposit (Android, iPhone) (Link)
Paypal: $1000/Day, $3000/Month (Android / iPhone) (Link)