It's a universally acknowledged fact that when you have had a break up you should "unfriend" your ex immediately. You can Google search "how to get over a break-up" as many times as you would like and normally the top piece of advice would be to unfriend or unfollow them from Facebook, Twitter, Pinterest, Instagram, etc. In theory, unfriending your ex is the most obvious thing to do; that doesn't necessarily mean it's the easiest and it certainly doesn't mean that everyone does it.
I posed this question to people within my own friendship circle, and though the results aren't necessarily scientific or universally true, they do throw up some interesting responses. When I updated my status asking people to send in their thoughts on the issue, I was expecting the answer to be overwhelmingly "obviously yes you unfriend them, what a silly question!" But instead I was quite surprised at the number of very measured responses I received, in the main a majority of people actually answered "it depends on the break up."
Of the people who answered, nearly everyone said that no single break-up is the same and it all depends on the context of the break up. If it was a really difficult one that ended on a sour note, then yes, if not and if it was more or less amicable, then don't. If the ex was very creepy, then the obvious answer would be to defriend but that doesn't mean that they won't try to add you again.
The general consensus among my friends was that unfriending seems a bit over-dramatic, and that provided you are OK with seeing your ex in pictures having fun, doing things without you, seeing them in pictures potentially with another person, and so on.
I have only ever met one person who actually unfriended their ex; the circumstances being that this person actually messaged his ex and said he needed the space to move on, and this person said that he realized defriending his ex for a certain period of time actually helped him move on, and he is now on speaking terms with the ex. Another friend actually created a friends list and changed the settings so that he would always appear offline to that list whenever he signed in.
The common sense move would be to unfriend your ex, and some psychological arguments would agree that it is the best thing to do. Even if you claim you are "over him/her," the temptation to stalk is always going to be there; you're always going to go through his/her photographs, you're going to take note of every status update, you're going to get jealous that some mystery guy/girl posted a message on his wall and put extra xo's at the end of their messages and so on. It's a never-ending cycle of paranoia and jealousy and common sense dictates that to spare you the pain you would be better off unfriending them for however long it takes until you are fully over your ex.
It's important to recognize the possibility that if you still have your ex on Facebook, chances are you still aren't totally over him/her, and one of the things people do to try and cover that up is overpost things (status updates and photos) in a bid to send out a subtle message that screams, "I'm better off without you, look at how happy I am without you in my life!"
Because so much of our lives goes on Facebook, the idea of unfriending someone does effectively feels like deleting some of your most happiest memories.
It wouldn't be in my place to lecture people on whether or not to defriend their ex-significant others (indeed I'm Facebook friends with my ex, but that's another story). That's a decision each individual has to make,and some come out of it unscathed, others not so much, but the presence of Facebook undoubtedly does make the healing process that little bit more difficult.