Ah, yes -- the zipper! A wonderful invention that is, recently, increasingly prone to failure. In fact, there seems to be an absolute epidemic of zipper failure going on. I don't know whether it is quality control in China and India, where most zippers are made, or just what, but if you're having zipper problems, you're not alone.
My first piece of advice is that you always zip a zipper closed prior to washing the article of clothing. It only takes a moment, and this is 'cheap insurance' because it reduces wear and tear on the zipper components during the laundry process.
In this section, I'm writing only about SEPARATING ZIPPERS, such as those found on most jackets.
If the zipper is not working
STEP 1: Carefully inspect the teeth of the zipper, as well as the hard starting point at the bottom that is inserted into the zipper pull on the opposite side of the opening. IF EITHER THE TEETH OR THE STARTING SLIDE ARE DAMAGED, the zipper will need to be replaced.
STEP 2: If the zipper teeth and the starting slide point are in good shape, then most likely the culprit is the zipper pull itself. These do indeed wear down over time, and it is far easier to replace a zipper pull than to replace a whole zipper, particularly in winter-weight jackets with multiple layers of fabrics.
NOTE: If you have a garment from a reputable outdoor manufacturer (North Face and Patagonia come to mind) they will often guarantee their garments for life. Contact the manufacturer of your garment and inquire if they will replace the zipper. If they will, you don't have to bother with any of this!
STEP 3: Remove the old pull. You'll notice that the pull is just on one side of the zipper. At the upper edge of the zipper on that side, there is a 'stop' which keeps the zipper pull from flying off your jacket when you close it. These days, this is usually a bar-like section of plastic that does not look like a zipper tooth or coil, although it may also be made of metal if you have a quality metal zipper. This 'stop' must be removed before the zipper pull can be removed. If it is plastic, I simply grab this bar with a pair of normal household pliers and break it off, sometimes with a slight twist to my hand that helps crack the plastic. It breaks up and falls away. If it is a metal stop, you may be able to actually pry it off using a fine screw driver to open up the metal seam that is clamped over the base tape material of the zipper. Some metal stops can be re-used, so don't throw it away. During this process, do your best to prevent cutting or tearing of the zipper tape, for it will fray if it is damaged, and you'll have to replace the whole zipper.
STEP 4: Unstitch the upper end of the zipper from the jacket. On a zipper, when the teeth stop, the base tape material of the zipper usually continues on for an inch or so further, with no teeth attached. This smooth end of the zipper tape is usually folded under, and stitched into seams of the jacket front. Using a seam ripper or a very fine pair of embroidery scissors, open up these seams at the upper end of the zipper until you can pull out the plain tape. You may have to remove more than one seam, including some top stitching.
STEP 5: Pull the failed zipper pull right off the now-completely-open end of the zipper tape. DO NOT DISCARD IT QUITE YET! On the back of each pull, there is usually a number. Also, the pull will have a very distinctive shape depending on what sort of teeth are on the zipper. YOU WILL NEED TO KNOW THE NUMBER AND THE SHAPE of your zipper pull to get the correct replacement. The number indicates the size of the zipper teeth, and the shape differs depending on the type of teeth on the zipper.
NOTE: In my experience, zippers on quality garments made in Europe seem to have pulls that are not the same as most domestic garment pulls. Don't be surprised if you fail to find the proper replacement pull for a European-made garment.
STEP 6: Purchase a zipper repair kit at a sewing notions store, or purchase an individual replacement pull if possible. We recently found pulls for sale individually at Pacific Fabrics in Seattle, and Seattle Fabrics also has individual pulls for sale. I have purchased boxes of multiple kinds of pulls in the past at JoAnn's Fabrics. It's a good idea to take your jacket and your old pull to the store with you.
NOTE Be sure to note whether your zipper has a double-headed pull or a single pull. They are sometimes slightly different, and you will want to purchase exactly the kind you had before.
STEP 7: With the correct pull in hand, carefully slide it back onto the zipper tape, reversing the actions in Step 5. Make sure the bottom goes on first, and that the pull lever is on the correct side of the pull. You will start out sliding the firm, woven edge of the zipper tape through the track, and then the slide will go down over the teeth.
STEP 8: Slide the new pull all the way to the bottom stop, and zip up the jacket as if you were going to wear it to make certain the the new pull is working correctly. Even tug lightly side to side to make certain the teeth are fully engaged.
STEP 9: When you're confident that the zipper works well, the next step is to replace or create a stop for the top of the zipper near the neck. Some zipper repair kits come with metal stops that you can pinch into place over the edge of the zipper tape, just past the position of the last tooth or coil. You can also form a stop by zigzagging over the end of the coil area, but be sure to create a bulky thread mass that will actually stop the zipper pull. Another possibility is to fold the 'eye' portion of a hook and eye set in half and sew it over the end spot. You can also sew a tab of small ribbon across the zipper tape to stop the pull.
STEP 10: Finish your repair by re-stitching the fabric around the zipper near the neck. Fold the end section of the zipper tape under as it was when you opened the seams, and then top-stitch close to the seam edge, and re-sew the decorative top stitching if there is any.
While this may read like a big hassel, replacing a zipper pull is MUCH easier than replacing a whole zipper! And it is a lot cheaper than buying a new coat!