I frequently get random friend requests, which I decline because I'm not sure who the Summoner is or how they got my name. I'm often curious how and why they added me, though, and I'm sure some of them would tell me if they had the option.
I play Xbox Live a lot and it has a feature that allows you to send a message along with a friend request. Sometimes I'll get a FR with an attached message that is something along the lines of, "Hey, I played with you a few games ago and you seemed cool so I thought I'd add you," or, "Hey I'm a friend of X's, they said we'd get along," or, "Hey, you added your name to the handle list on [insert forum] and I'm a member there too".
I'd love a similar feature on LoL, I'm sure I'd have added a lot more people by now if only I knew why they were adding me. I can't think of a reason why we don't have this so I thought I'd throw it out there.