What problems can occur if I accept Facebook friend requests from strangers?

[Newbie]

About a week ago I got a Facebook friend request from someone who lives in the same large apartment complex where I have my office (the complex rents out about 8 offices). This guy's Facebook page indicates he is originally from Berlin, Germany but now lives in the U.S. Both of us are friends of the apartment complex on Facebook and I guess that's how he found me. I thought he is probably a lonely foreigner in a strange country and I didn't see any reason to reject his request. After I accepted, he sent me an email message thanking me for accepting. I sent him an email thanking him for sending the request. Besides, I would like to have as many Facebook friends as possible.

Today, I found out that I have two more friend requests from people I don't know. One is a guy from England. Is there any reason I should not accept these friend requests? Is it fairly common to get friend requests from strangers? Is there any kind of Facebook scam or fraud that someone can pull just by being friends on Facebook? Also, I was thinking that maybe the guy from Berlin told the two other guys that I accept Facebook friend requests from anyone and that's how they could have found me.

One strange thing is that I can't find the last two friend requests on my Facebook page - they're just in my Outlook emails. The friend requests do seem to be authentic Facebook friend requests, though. The only information that can be found about me on my Facebook page is name, education, city where I grew up, city where I live now, and my occupation. I don't have my birthdate up on my Facebook page as that can help an identify thief. I don't even identify any friends as family members or best friends - they're all just in one big list as I want to limit the information I give out. Thanks for any information you can provide.