I'm currently working at Customer Service for Nextel, so when people call in to either complain about their cell phone, troubleshoot it, or pay a bill, they talk to my department. I haven't been working there very long, so the stories I have aren't quite as amusing as other people's:
On November 3rd of this year, I got a call, but no customer was on the other end of the line. Instead, to my surprise, I heard the concession speech of John Kerry. Needless to say, I was quite surprised, as was my supervisor who I waved over.
I had one customer whom I had to explain her bill to while she was sobbing her heart out. As it turned out, it was because the last representative she spoke to about it made her feel stupid...when she called in the previous day.
I've also had my share of angry customers threatening to sue, change carriers, etc. But none stick out enough to warrant mention here.