ING
I've had an ING bank account for almost two years now. For the uninitiated, it's an online bank full of awesomeness. I have a savings account there that is making about 4.5% (and that rate goes up every month or so.) They also have a bunch of mutual funds with no management or trading fees, a couple of which have made 40% for each of the past two years. Not too shabby eh?
I just got an email announcing that I can now open a checking account with them too. Currently I have a normal bank, and ING is linked to my regular bank. I can transfer money in and out as needed. Theoretically now you could use ING as your only bank (although I'm not quite sure how you would cash/deposit a check.) They offer free ATM access and they'll write/mail paper checks for you.
I have been nothing but impressed with them. I've made a lot more money than I would have if it sat in my bank's savings account which currently earns 0.2%. Yawn.
If you are interested in giving it a shot, contact me for a referral. They'll give you $25 and I get $10 out of the deal.