I’d like to get into online banking. I, however, know nothing about it. You should all educate me about it, and recommend me banks. 
I’ve been using ING Direct for my “immediate” savings fund - in other words, the money that I’m going to need for car insurance in 6 months or car tax or whatever, and that theoretically I’m going to start putting money into for instant-access savings. I like it. You need a real brick-and-mortar bank account to link it to, but it’s no fee. You can get your money in and out in 48 hours. It gets like 4% interest or something. Very easy to use and does what I need it to do.
Ditto what Zsofia said. I’ve been quite pleased with them.
I had been using ING for a while as they had pretty good interest rates, but about a year ago I switched to HSBC as they have the highest (that I can find) without any minimum balance or account fees. I believe they’re paying 5.05% right now on their savings accounts.
I use GMAC for my savings account. They have competetive interest rates (currently 5%) and are one of the more user friendly online banks. The big ones have already been mentioned: GMAC, ING, HSBC.
For a more complete list, check out the Fat Wallet forums. Specifically, this thread which maintains a list of banks, interest rates, and minimum balances required to open an account.
Your regular bank probably offers online banking. You should check with them about it (assuming you like your bank).
Emigrant Direct’s APY is 5.15% right now. No fees, no minimums. We’ve been very happy with our account there.