Even with internet banks, the rate available to savers is not great. For example, one of my banks, ING Direct, is paying about 1% on their savings accounts and CD rates top out at 1.25%. While the 1% interest rate easily demolishes the 0.20% rate paid by Bank of America on savings accounts, the after tax return is barely worth the effort.
Instead of putting money in savings vehicles like CD's and/or money market accounts, I recommend directing any excess cash to paying down debt. Instead of earning 1% on savings, you can save 15% on credit card debt, 4-7% on car loans, and 5% on mortgage loans by reducing the principal balance of those loans. The only downside is that you may give up some flexibility by paying down the principal on a loan. Think about it this way, the mortgage company is not going to let you get the $1,000 principal payment you sent them with your tax refund money.