As the person who answers the phone in an office where the project managers are often away from their desks/inaccessible, I have a special pet peeve.
I don't particularly like answering phones in general. But the WORST is the caller who asks for a specific person. I politely say he/she's not available—would you like voicemail? And the caller pauses, then says, "Well, maybe you can help me ..." and launches into a long explanation of what he (or she) needs concerning something I know nothing about. So now that he's made his problem MY problem, I have to run around the office and try to get answers, even though I don't have them because—guess what?—he needs to talk to the person he called for in the first place.
For the record: No, I can't help you. So stop asking.