Amber parking lights always on

The amber side marker/parking lights on my '96 Legacy Outback are now staying on all the time, even with the car off and the switch turned off. I need to either remove the fuse or disconnect the battery to get them to go off. What is the likely problem, and how do I go about diagnosing it? Is it likely that I'll need to buy a new headlight switch for the steering column?

Look at the top of your steering column. There's a switch there for your parking lights. Rock it towards the driver to turn it off.

I have this exact same problem with my 96 Legacy Outback and the parking light switch does not seem to make them go off. The lights either stay on solid with it in one position or they blink when the switch is in the other position. Does anyone know if this is a problem with one of the fuses?

The headlight switch is your most likely suspect, the ignition should still shut the lights off when they are turned on by the switch Jay is referring to, although all the lights are disabled when I shut off the ignition in my subaru, therefore it may be an issue with your ignition switch or a stuck relay.