I was flying LGA-ORD-PDX this past weekend, and while usually I would bring my rollaboard as carry-on, I decided to check it as I had other bags anyway. When I landed in PDX, it was actually one of the first bags off (despite what you read here, I guess the priority tags occasionally work). The only problem was that while the bag itself had arrived, upon attempting to roll it away, I discovered that the wheels had apparently been shorn off en route.
I went right away to the baggage office, described what happened in about two sentences, and the agent took one glance and immediately told me, "Normally we are not responsible for that type of damage, but since you are a priority customer, let me go see what I can do." She goes into the back, and comes back a minute later holding a brand-new rollaboard. The whole encounter took 2-3 minutes, and I left feeling very happy that I continue to stay loyal to UA. Great customer service!!

On a related note, I got her name (turns out she is the Service Director there) - where is the best place to send an email/letter to about this? I would love for UA to thank her on my behalf, as employees like this should always be encouraged.