Use the phrase "happen to ___" to talk about something that doesn't seem very likely. One way this is useful is for asking questions, even though you don't think the listener will know the answer:
Do you happen to know a guy by the name of Fred Breedlove?
In this example, you ask "Do you happen to..." because you think that the listener probably doesn't know this person. You would ask this question if this person was from the same town as Fred, or went to the same large university as Fred, or worked at the same large company.
You can also use "happen to ___" to ask questions politely, even when you do think the listener's answer will be "yes":
Excuse me, would you happen to have a pen I could borrow?
"Have", "see", and "know" are the most common verbs that follow "happen to".