For his book The Visual Miscellaneum, David McCandless, along with Lee Byron, had a look at breakups on Facebook, according to status updates. They looked for the phrase "we broke up because" in status updates, and then graphed the frequencies over time. Why they couldn't just look at updates to relationship status, I'm not sure.
Notice the peak leading up to the holiday season and spring cleaning. Then there's the people who think it's a funny April Fool's joke to say the broke up with their significant other.
Finally, there's the highlight of Mondays, which you might lead you to believe that people like to call it quits during the beginning of the week. My hunch though is that it happens towards the end of the week, people use the weekend to be sad, and then talk about it on Facebook.
[Information is Beautiful | Thanks, Elise]