I just got a friend request from somebody I don't recognize. If they'd been able to put something like "I played the most amazing game with you yesterday!" or "I'm friends with MrCoolGuy and he told me to friend you too" on it, I might be able to figure out where they came from.

So, with that in mind, I would love to see an optional "Reason:" field added to friend requests.

I must agree on this part. This would symplifie it. Small text of 1 sentence should be addable.
!support this thread.