The Mutual UFO Network, or MUFON (pronounced moo-fon) was founded in 1969. The headquarters for the non-profit organization is in Denver, Colorado. In a nutshell, it's a bunch of people who study UFOs, or Unidentified Flying Objects (flying craft in the sky that, well, are difficult to identify) which are generally thought of as flying saucers or alien spacecraft - although there are varying theories as to what they could be. If you want the fancy explanation, according to their website, MUFON is "dedicated, through its volunteers, to resolving the scientific enigma known collectively as unidentified flying objects."
Depending on your level of skepticism, these folks are either scientifically thinking people dedicated to the study of a fascinating phenomenon...or a bunch of loonies wasting their time. Indeed, depending on whether or not you believe our planet might be visited by extraterrestrials (space aliens), you will hold what they do in high regard or laugh it off. Whichever is the case, they are serious about what they do and have a high level of organization in their policies and protocols in regards to how they conduct their investigations and themselves. Their investigators are trained using the "MUFON Field Investigator's Manual." It is 300+ pages long and instruct on witness reports, identifying hoaxes or misperceptions, handling sensitive evidence, and abduction claims and claimants. To become a full-fledged Field Investigator they have to pass a 100-question, open-book exam (didn't you used to love those back in school?) based on the handbook and their own aircraft observations.
The network of investigators in MUFON are considered "ufologists," one of the many terms now in our lexicon derived from "UFO." Concurrently, "ufology" is the study of UFOs, or the business that ufologists deal in. The network isn't just their official investigators, but it also a vast group of people interested in the phenomenon (anybody can join for a fee) or individuals that have actually seen -- or claim to have seen -- UFOs. Members are all over the world. There are chapters in Mexico, Canada, Australia, Great Britain, and 32 other countries from Austria to Zimbabwe. They have regular symposiums and conferences attended by very diverse groups of people. They have two publications: the monthly MUFON UFO Journal and the International UFO Symposium Proceedings.
The mufon.com website was not very informative as to their history. The founding year was the best piece of information on that subject that I could find. It has an interesting section in the FAQ about what to do if you see a UFO. MUFON is honest about the fact that it's possible that the sceptics are right and it's all a modern myth of our own making, which is why, according to Dennis Stacy, a former editor of the MUFON UFO Journal, the phenomenon is approached by MUFON dispassionately and from a variety of different angles.
I personally feel it is a worthy cause. Something's going on up there, but I would never be so presumptuous as to say they're alien spacecraft. They could be, or they could be top secret experimental avian military vehicles. Whatever the case, I don't object at all to any organization dedicated to studying, as long as they do it seriously, what exactly is flying over our heads. They are, after all, endorsed by none other than Dan Aykroyd, and who are we to argue with a Blues Brother, huh? :)