I have a 2010 Honda Ridgeline. The other day we rec'd about 2-3" of wet snow. WHile I was brooming off the passenger side I decided to turn the vehicle on by reaching over from the passenger side. I didn't realize the wipers were turned on from the day before. When the truck started the wiper on the passenger side broke free from the snow/ice but the driver side wiper remained frozen to the windshield. Before I could turn off the wipers they had cycled twice and now the driver side does not work but the passenger side works fine. Did I shear off a gear or pin of some kind?

SOURCE: my driver side windshield wiper

I just solved this problem last night with my '05 Impala, and ultimately the solution was what newton5083 stated above.  Yet, it may also be this (I found it online somewhere):
You have bent or broken the "park tab" on the windshield wiper motor bracket. The correct way to fix this is to remove the wiper arms, wiper linkage and wiper motor from the wiper motor bracket, and install a new bracket.
I just bent the tab back into place a couple times for our daughters 2005 Impala but it kept getting bent down again when they didn't take the time to make sure the wipers were not frozen to the windshield, or tried running the wipers to remove heavy snow on the windshield. So yesterday I fabricated a small piece of metal and bolted that to the bracket in the same place the tab stop was.
If someone wants to access this bracket and tab-
1. Use a ½ inch or 13mm socket & ratchet or wrench to remove nuts on wiper arms.
2. They may make a special tool to remove the arms, I used a screwdriver and hammer to tap bottom of the arm to wedge them apart from the spindle.
3. Two small button-looking clips hold the drivers side cowl cover in place under the windshield. These are two-piece clips, pry up the center, than the outer piece.
4. Unclip the washer hose from cowl cover, than pull out plastic cover.
5. There is a smaller plastic cover with on plastic button head holding that cover in place. Gently pry under that clip to remove that cover.
6. Now you can see the wiper trans and bracket. You should see a small tab on that bracket that looks pushed down and bent or possible a square small hole with some torn off metal where the tab broke off.
7. Remove small plastic cover over the wiper transmission and you can see a small spring-loaded arm underneath the wiper transmission assembly.
8. You need to find something to pry that tab back up so when the wipers are running that spring loaded little arm just snaps past the tab running clockwise. It's when you shut off the wipers that the wiper transmission assembly reverses rotation counter clockwise and the small spring loaded arm underneath hits that tab stop, than the wipers will go all the way down and shut off as they should.
Once that tab stop gets bent out of the way the little spring loaded arm has nothing to stop the wiper transmission assembly so it keeps traveling counter clockwise until some other stop shuts the wipers off straight up on the windshield.

There is a revised bracket part # which is supposed to be more durable, GM part #12368639. Here is a copy of the TSB which points out this problem:
Bulletin No.: 05-08-43-003A
Date: March 10, 2005
TECHNICAL
Subject:
Windshield Wipers Park in Up Position (Replace Windshield Wiper Motor Bracket)
Models:
2005 Chevrolet Impala, Monte Carlo
Supercede:
This bulletin is being revised to make a correction to the Parts Information. Please discard Corporate Bulletin Number 05-08-43-003 (Section 08-Body and Accessories).

Condition
Some customers may comment that the windshield wipers park in the out wipe (vertical) position.
Cause
This condition may be caused by a bent park tab on the windshield wiper motor bracket.

Correction
To correct this condition, replace the wiper motor bracket. It will be necessary to transfer the following parts listed below to the new bracket.
^ Wiper transmission
^ Wiper motor crank arm
^ Wiper motor
1. Remove the windshield wiper motor drive system module.
2. Remove the windshield wiper transmission from the windshield wiper motor bracket.
3. Remove the wiper motor crank arm from the windshield wiper motor.
4. Remove the windshield wiper motor from the bracket.
5. Install the windshield wiper motor to the new bracket.
6. Install the wiper motor crank arm to the windshield wiper motor.
7. Install the windshield wiper transmission to the windshield wiper motor bracket.
8. Install the windshield wiper motor drive system module.

A TSB is not a recall, if vehicle is still under warranty the dealer should be repaired for free. If not, you'll have to pay for the repairs. 

SOURCE: Driver's side wiper froze and broke on PT Cruiser.

on the wiper arm at the bottom is a plastic cap. remove it and underneath is a 13 or 15 mm nut line the wiper back up and tighten the nut. the wiper should work.

SOURCE: Driver's side wiper froze and broke on PT Cruiser.

There is likely something in the linkage between the wiper and the motor that is broken.