I don't think there's anything out there quite "like" ING Direct: so if you're asking about them in particular, the answer might be a little different from other kinds of "online banking" experiences. There were a few examples early in the bubble of "totally online" (i.e., branchless) banks, but none (AFAIK) have survived. ING Direct (through their Orange Account product) have really put a stake in the ground: there are no fees for ANYTHING you might want to do (though there's not much you CAN do!), and it's really just a "cash management" account. You can find cash management functions in most brokerage products, but the ING (current 2.2%) rate is much higher, and there's this business of all the fees and complications. On the down side, you don't get an ATM card, checks, etc.: they expect you to do your othar-than-cash-management functions in some other account. They just ACH funds to and from that account.
It's a brilliant move: retail banks are fighting about "no fee checking" and are incurring large costs for typical customers (call your bank about a question or problem? It likely costs them $10 to answer the phone!), so they aren't involving themselves in any of that (though I notice you can do a transfer over the phone, hmmm, that's expensive), but unless you have a lot of cash floating around and can benefit from the additional interest (the example on their home page is $440 on $20k in a year vs. about $90 for a standard "savings account" that you might have linked to your checking account) it seems like a lot of work to transfer things around and keep track of.
What are your concerns?
/jordan