Most established banks to dump $ into high interest saving acct?

[Daniel R.]

What are some of the most established or reliable banks out there to put money into a higher interest yielding savings account?  Not necessarily looking for a CD that locks up money for 24/36 months, but rather a fluid account that yields better interest than a standard money market that gets 0.02% interest.  What are the fees, penalties, or other main factors to consider with these accounts?  Thanks!