Yes, my wife and I have been using Security First Network Bank for about a year. No problems whatsoever. SFNB is the first internet only FDIC insured bank. They do, however, have one branch in Atlanta. This turned out to be indispensible when we needed a cashiers check to close on our house.
I suggest doing what we did. Open a checking account and use it in parallel with your existing one to see if you like it.