Right now interest rates are being held down by the fact that the Federal Funds rate is targeting 0% Normally banks are able to get money from a central bank or from deposits at a low interest rate and then lend them out at higher interest rates and make money on the difference.
If you search rates right now you might find things like:
checking accounts interest rates (if they are paying interest) below 1% and often very close to 0%.
Certificates of Deposit between .75% and 2% though you might be able to find some slightly higher, I've been unable to find anything higher than 2.5%
Savings accounts also are offering very low interest because banks cannot charge very high interest on their other products like mortgages or business loans so they have to keep the interest they are paying out low as well. You might be able to find a savings account that is paying between 1 and 2%.