We switched about a year ago to ING Electric Orange checking. We've already been saving online, so checking was the next step. However, the transition has not been as complete as we would like.
First, let me state the advantages. One is the interest rate, which is much higher than anything you would find with a traditional checking account. The next advantage ING has over other online banks is you can subpartition your accounts, so for example you could create a Christmas account. This makes budgeting a lot easier. Also, you can have automatic bill pay, but I believe that's something most banks offer nowadays.
We've liked using this account for all our major, recurring bills, such as the mortgage and student loan payments. However, it doesn't work well for sudden expenses. You don't have a checkbook - all the checks have to be ordered online and take about a week to arrive. So we've found ourselves keeping our old checking account open to handle last minute check writing.
I would recommend this account to anyone who wants a higher interest rate earned on the money that you spend on recurring bills every month. However, don't make it your only account. And if you're not comfortable handling all finances electronically, this is not the option for you.