Help! I have a 2002 Ford Explorer and the brake lights are stuck on. Does anybody have any ideas on how to fix this?

Spray the brake light switch, located just above the brake pedal, with WD-40.

Do you mean the brake light in the dash is constantly on, or the brake lights at the rear of the vehicle are always on? If the lights at the rear of the vehicle are on, are you sure it's the brake lights and not just the running lights?

You can unplug brake switch connector on brake arm to verify switch is staying on, if brake light goes out, it Is the switch, if you unplug and it stays on, it it not likely the brake switch.
Most vehicles? Combine brake/turn and goes not only through the signal head, but the 4 way flashers as well.

I believe this has the foot operated emergency brake pedal. Try putting your foot under the pedal, pull and hold the release lever and lift the pedal up. Sometimes after the emergency brake cable stretches some, the pedal does not come up all the way upon release.

That is of course assuming that you have already had the brakes checked out to make sure that they are not bad and causing the light.