As long as you use a legitimate online bank that is FDIC insured, you are just as safe as the bank down the street. I use ING Direct myself for my savings that I'm trying to build for long term. You can still get it within a couple days but it's not quite as easy as running down the street to the ATM.
With this particular bank, the account is attached to your main bank account so that you can deposit or withdraw your funds as needed. The interest is only around 2.5 or 3% right now but it's still better than a regular savings account.
If you open one, try to deposit at least $250 because they are giving a $25 bonus or they were when I opened mine. Nice 10% earnings right then and there.