Sounds like it is either of these:
Manual Control: Blower Motor Resistor
Auto Temp Control: Blower Motor Power Module
In either case, if you disconnect the power wire from it, the blower motor should shutoff, and this usually indicates a problem with the resistor or power module, which ever you happen to have. You can limp along without the resistor or module, as the blower motor will still work, but only on the HI setting. The resistor, or module, are located near the blower motor under the dash.
There is a more comprehensive test for them, but I have forgotten what it is.