DaveGod-
Your question depends on where you live-
In CA, there are wells fargo, bofa, and wamu (one of the biggest bank, --> Lots of ATMs)
I only have bofa account since I do have direct deposit each month- I use their online service, which is also good. However, they do charge a lot if you don't have direct deposit or maintain any balance. I could be wrong, you may wanna ask any student account-
The best bet is Wamu they are totally free checking account.
For savings- I have been using solely ING Direct. They have the highest interest with no fee at all. the requirement is you have to have a checking account from other bank. They only link your saving to your checking. (No ATM) So, if you have to deposit or get your money, it has to go through your checking account-
Right now, they are having promotion to open savings account (you'll get $25) however, it has to be referred by an account holder- (PM me if you are interested)
EDIT: ING Direct has 5% interest! NO fee and no minimum (some people even open with $1 and get the $25) FDIC insured (I check it through FDIC.gov) The company's world headquarter is located in netherland. One of the biggest group tha you may heard is the ING Barrings which deal with the stock market.