The Friend From Middle School
Never mind that you haven't spoken in seven years. All this guy had to do to find you on Facebook was remember your last name, and boy is he excited about it. He will at first attempt to rekindle your friendship through a flurry of wall posts and comments on your pictures. However, things should calm down pretty quickly once he realizes you don't have much in common anymore and you remember that you only used to hang out with him because his parents let him listen to Blink-182.
Most common Facebook interaction: an annual wall post on your birthday containing a reference to something you both liked or did in 7th grade and some variation of the phrase "we should hang out next time we're both back in town."

The Stranger
"Stranger" here doesn't just mean someone from your school who you don't hang out with or know anything about. No, we're talking about a person who you have literally never seen or spoken to, whose existence you were not even aware of until they friend requested you. Why they did this, along with how they managed to find out your name, remain some of life's great mysteries, as most of these friend requests go unanswered.
Most common Facebook interaction: most interaction stops with a denial of their friend request, although I imagine if any are accepted it consists of the occasional poke and multiple requests for credit card numbers and/or organ donations.

The Guy You Swear You Know From Somewhere
You know, that guy? His name's Joe, you had bio together freshman year, you think. Or was it chem? No, wait, that's not it, you met at that Phi Delt party a few months ago. Yeah! You were both just chilling by the keg, and then you wound up playing a couple games of pong together. Wait, what? That was Steve? You sure? Well who the fuck is Joe then?
Most common Facebook interaction: tagging him in a "25 Random Things About Me" note, in hopes that one of his things will be how the two of you met.

The One You're Actually Friends With
You have a surprisingly small amount of these and generally don't become Facebook friends with them until years after you've been real friends. This is mainly because through such radical practices as conversation and hanging out together, you have somehow managed to learn each other's interests, activities and sexual orientations without the aid of a Facebook profile. These friend requests are thus largely unnecessary and mostly just done for ceremonial purposes.
Most common Facebook interaction: one wall post expressing surprise that you aren't already Facebook friends followed by very little else after you realize it's not that enlightening to find out that the guy who confided in you when his parents were getting divorced likes Chuck more than you thought.

The Excessive Application Adder
There was a time not too long ago when you liked hanging out with this person, but somewhere in between the superpokes, the mob wars invites and the graffiti posts you completely forgot why. His obsession over adding every application Facebook has to offer and his insistence that you add all of them as well have completely overshadowed any redeeming qualities he may once have had. Sure, borrowing his psych notes is nice, but so is not having to turn down six new requests every time you log in to try and find out who Joe is.
Most common Facebook interaction: ending your friendship after the ninth invitation to play gangster battle.

The Old Person
This is generally one of your parents doing a thinly veiled job of trying to check up on you or a professor at your school trying to "connect" more with their students. They find every bumper sticker and lolcat they encounter unique and hilarious and would love to share all of them with you, if only they could figure out how. They also have no concept of the term "limited profile," so expect a lot of questions about why they can't see those pictures of you on your alternative spring break to Cancun.
Most common Facebook interaction: a paragraph-length wall post with meticulously checked grammar and enough questions for at least three installments of "Parents Just Don't Understand."

The Hot Girl
You said something that made this girl laugh once and made sure to friend request her within minutes before she forgot who you were. Her favorite music, TV shows and movies make you want to puke, but that hasn't stopped you from working references to all of them into your frequent posts on her wall that she hasn't gotten around to replying to yet. Now if she would just put her class schedule up so you could have an easier time "accidentally" bumping into her…not that you're Facebook stalking or anything. Seriously, guys that do that are pathetic.
Most common Facebook interaction: special alone time with those pictures from her alternative spring break to Cancun.