Ally: http://Ally.com
INGDirect: http://INGDirect.com
Fidelity: http://personal.fidelity.com/accounts/aong/fcma_learn.shtml
Schwab: http://www.schwab.com/public/schwab/banking_lending/checking
Everbank: https://www.everbank.com
Alliant FCU: http://www.alliantcreditunion.org
Incredible Bank: http://incrediblebank.com
Salem Five Direct: http://www.salemfivedirect.com
Bank of Internet: http://www.bankofinternet.com
PerkStreet: http://www.perkstreet.com
Personally, I'd go with Ally. Free ATM rebates. Competitive interest rates. Easy to set up automatic transfers to savings. Free ACH transfers. Remote deposit being rolled out now.
You can't go wrong with any of the other banks either (ING and Schwab are great also), but Ally really has a nice offering.
Also, be careful when and where you use your debit card.
If someone gets a hold of your debit card info, they are accessing your cash directly. With a credit card, they are creating a future liability (no cash out of your account). Further, the consumer protections are not nearly as good on debit cards as they are for credit cards.
I talk about this at length here: http://www.seedlingfinance.com/443/why-i-always-use-a-credit...