I've only ever had 2 'strangers' try to befriend me... just ignored them... there's a vague possibility they knew me years ago, as both were from a certain (huge) workplace... but didn't ring any bells, so ignored.
The rest are mostly family and (real-life) friends, pluse one or two long-lost mates who I really would like to see again anyway.
The kids' friends sometimes try to make friends, but I just explain that they wouldn't want to know all about an old fogey like me anyway...
I only have one workmate on there too... he is a mate outside of work... the rest of the time I'm happy to leave the place far behind me!
I recently took off all the friends who never seem to use it... what's the point? And whenever I come across someone who's worried about using it, privacy etc, I just say... spend a wee bit of time working out who you sdon't mind seeing what, and apply those filters... it isn't that difficult. If you don't want anyone to see or know something, don't put it up. And if you still aren't happy, stop using it!
I like using it personally, and it's a great way of keeping in touch, especially as I live a long way from other members of my family.