Why does your brake light stay on?
If you're talking about the stop lights, the red ones on the back, that happens because your stoplight switch is stuck. Not usually a difficult thing to fix, and if you're somewhat handy you can save quite a few bucks by replacing it yourself. If it's a Ford, it may be a little to a lot more complicated.
Please fix it soon, because drivers behind you won't know when you brake.
The stoplight switch is usually located under the dashboard, above and behind the brake pedal. When you step on the brakes, the switch is activated, turning the lights on. When you release the brake pedal, it's supposed to disconnect, turning the stop lights off.
To troubleshoot using the process of elimination, crawl under the dash, locate the stoplight switch and disconnect ONE of the wires leading to it. BE CAREFUL - don't touch the wire, the terminal nor the pliers you may be using to ANYTHING metallic. If you happen to remove the "hot" wire, the one that is hot all the time (the wire that provides power from the battery to the switch, as opposed to the wire that goes from the switch to the stop lights, which should only be hot when the brake lights are on), it will cause a dangerous arc if it touches metal.
You can avoid that problem by disconnecting the battery before removing the wire. Caution: Turn everything electronic, e.g. stereo, etc. off before disconnecting the battery.
After disconnecting the wire from the stoplight switch, re-connect the battery momentarily. If the stop lights don't come on, the problem is in the switch.
The people at an auto parts place usually are very helpful in explaining how to replace things.
on my 03 Elantra, there is a plastic "spacer" that the tip of the switch touches to turn off the switch(brake lights) off. Plastic spacer crumbled and replaced it with a nut and bolt that had the same thickness. Problem solved.