I've been using online banks since 2005 when I was getting 5.5%. I was with HSBC for along time, but they started cutting back on their interest a lot and service.
I then moved to GE Capital, which sold to Goldman Sachs. I think I am around 1.35% right now. I like the product a lot, transfers are fast and easy, the interface is good, you can wire money into and out of the account, etc. With GS this isn't as necessary since the transfers are a lot quicker, but we have our paychecks go into a local checking account, pay our bills, then transfer the rest to GS. We leave about 1K in checking and about 5K in a local savings account, just in case. Any legit online bank will be FDIC insured, but be sure you check.
As far as ATMs go, I had a card with HSBC that I never used. You can only legally withdraw from a savings account 3 (or 5, can't remember) times a month. If you withdraw more than that a couple of times, they can close your account (true of ALL banks). So you shouldn't be using an ATM card against a savings account. Leave enough money in a local back that you would be covered for any large ATM draw.
The high interest checking accounts sound great, but most have a maximum account balance. So if you are over that max, your rates are terrible.
As an added perk, when you tell people that you have an account with Goldman Sachs they automatically think you are a baller. Even other banks. I did some work with some estate lawyers this year and even they acted impressed.
Edit: If you are thinking about CDs have a look at US iBonds. Right now they are paying out 2.65%, but you have to hold them for a year and you can only buy $10pp/yr.
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