I started using Everbank as my primary bank about a year ago when either Forbes or the WSJ did a story about it. So far it's been a good move for me. I had been looking for an online bank that would fit my nomadic lifestyle, but none I'd seen prior to Everbank had paper checking accounts. The interest rate on the checking is great, as are the rates for CDs. Not only can you bank through Everbank, but you can trade through the same account with Evertrade. I've bought stocks with Evertrade, but I've since decided to stick with Ameritrade for trading due to its more mature brokerage platform.
One of the best things about Everbank is its One View page, which displays all of your assets (including non-Everbank assets) and liabilities. This makes it easy to track activity in all of your accounts on one site, and shows your current net worth based on daily updates from your other financial institutions.
Did I mention Everbank's easy-to-use bill paying feature.
I recommend Everbank to anyone still lending their money to brick-and-mortar banks at no interest. With the exception of the weak trading platform, Everbank has been nothing but positive to me.