It's not new, really - the idea of online banking. No drive through tellers, no big brick building with security guards and alarms and cameras high up in the corners. These online bank alternatives are still protected by the FDIC (I know, I know - for whatever that's really worth these days), and some have been around for several years now.
Bargaineering has a nice list of the top online banks in their opinion. Checking, savings, minimum deposit, fees.
MSN has created a best online bank list as well -- they give lots of details about online banks versus traditional institutions, including features that may make internet-only banks more palatable for you than your mother's store down the street.
Consumer Search reviews the service of online banking, without distinguishing online-only from brick and mortar. The results? Bank of America comes in first, but an online-only bank, ING Direct, comes in second. They've also compiled a list of their best internet-only banks (after ING comes Ally, if you're interested).