LinkedIn is a legitimate business social networking site, but it isn't perfect! To wit: about a week and a half ago, I got asked to connect from someone who sent me a very suggestive email in my linkedin mailbox. What made it suspicious aside from the content was that legit connections are sent to me through my work email.

Both LinkedIn and Facebook advise you only to connect to people you know in RL. I think highly-trusted online friends can be included, particularly if you've connected in other ways (gift swaps, Christmas cards, etc.)

Facebook will block people from trying to "friend" you if you declare you don't know them when you decline (at least as of a couple weeks ago!)

Best protections: change passwords often. (A rule I honor more often in the breach than the observance!)