I've just found an article on one of Italy's most popular newspapers, the "Corriere della Sera", which states that emergency landings are far more common than is normally believed: according to it, at Heathrow there's at least one emergency landing per day. I find this number incredibly high. Is that true?
The article (which is more a collection of "quick facts") doesn't specify the source. I've turned to Google for further info, and the only result I've found is an article by The Telegrpah, which states that the average at Heathrow is slightly above one per week. Even assuming the Corriere journalist wanted to report that figure but got confused and accidentally wrote one per day instead of one per week, it still sounds very high.
An article on abc7ny.com (no idea how reputable that site is) mentions 66 emergency landings at JFK, 50 at Newark and 34 at LaGuardia over a 20-weeks span, from February to June of 2011.
So, if we only consider airliners, how common are emergency landings really?
As pointed out by UnrecognizedFallingObject in a comment, it depends on what is meant by "emergency landing". Is there a commonly accepted definition? If not, since we have to draw a line, I'd say a Mayday counts for sure, and I'd also include a Pan-Pan. Below that, I think we can ignore it.