Update: This Instructable was featured on lifehacker.com! Visit the article here.
The wheel on my favorite carry-on bag had a chunk come off of it one one trip and it wasn't too many trips later that the plastic part of the wheel came off completely, leaving behind the little metal core that housed the bearings. This left me scraping through the terminal and carrying the bag through anyone's house as to not leave a trail of scrape marks behind me. Other than the wheel the bag was in fine shape so I hated to throw the thing away. Here's what I did to repair it. You can see this repair and more than 300 others at my website at ShareYourRepair.com
Step 1: Bum Wheel
Here's what I eventually was left with on my carry-on bag--a bum wheel. It changed the meaning of carry on to "always carry" because the thing sat crooked and was obnoxiously noisy too. Now, if you only have a chunk out of your wheel like I did originally you may need to go ahead and put the thing out of it's misery and just pry off the rest of the wheel so you are left with a round base. I don't think you can do anything with the lumpy wheel unless you want to try to build it up with something but that's for another instructable.
Step 2: Wrap the Metal Core With Strips of Duct Tape
If your wheel is missing like mine, and what you have is uniform shaped:
Start a tear in the duct tape so that the strip is just the right width to cover the wheel. You can tear off about two revolutions of the duct tape and then it begins to get too narrow. For me I was able to get three strips from one width of duct tape. Wrap up the wheel until it is the same diameter as the other wheel.
If your wheel is lopsided:
In the case of a lopsided wheel you'll need to either break off the remaining wheel or return the wheel to round shape (which is a whole other deal) if you're going to repair it the way I did.