I use internet banking for almost all transactions in the UK - including payments to and from friends and family as well as to my other banks (I have a current (checking) account with 2 different banks, mainly from the fact that many years ago when you couldn't use ATM cards in all other machines which of course these days you can).
To be honest I am surprised that this isn't common practice in the US. Maybe because over here cheques are really being used in so few places these days that electronic banking is just that bit more popular?
Jason