This is a fairly common occurrence. If you carry some tools in the car you can usually fix the cable in about 10 minutes. It commonly breaks off a short piece at the back end where the cable flexes at the input trunnion. Loosen the cable at the front end, pull it back a little at the input end, and re-string it through the input trunnion fitting. Clip a small vice grip on the broken end of the cable, then readjust the output end, and you're on your way.

If you drive a lot, carry a spare throttle cable with the tool kit, as they tend to break at 15,000 to 20,000 miles. I have been scratching my head over this problem for years, but so far it doesn't seem serious enough to bother fixing. One cure would be to install an anti-friction bearing on the input trunnion mounting so it can rotate freely in the arm to prevent the cable from flexing. Another fix might be to install a sliding guide on the trunnion to maintain the orientation while the input arm swings.

If anyone has a better idea for an easy fix, do tell.

If the cable breaks at the output trunnion, you will need a little extra length on that end to reconnect it. Pull the outer jacket forward until the inner cable disappears well inside out of the way. Cut 1/2 to 3/4 inch from the end of the outer jacket. Then put the outer jacket back into the bulkhead fitting, push the inner cable forward to expose the output end, and reconnect it. This may work once and still have enough cable length to be serviceable, but don't push your luck for a second time. At your earliest convenience, order a new throttle cable for a spare.

Addendum, May 2010:
It is common to find fraying of the output end of the throttle cable. Single strands of the wire may unwind and break or cause binding in the outer jacket. This can be prevented by applying a touch of solder to the end of the wire. Tinning the wire to make the solder stick is easier done when the part is new.

On 5/15/2010, Jeremy in Australia offers this suggestion:
"You could possibly solder the point at which the nut tightens onto the cable to increase its strength and stop the strands from separating. Will have to give it a good clean and use some flux to get it to wick, then clean off any excess with a blade".

That is same as the prior paragraph, except he may be thinking to run the solder farther up the wire to include the area under the nut on the cable stop. This brings up another idea for an improvement on the input end of the cable. You might tin and solder the wire for an inch or so next to the input end. This could stiffen the wire in the area most prone to flexing and breaking. I will try this next time I replace the cable. Check here again for a follow up report in a few more years.