Area 51, Nevada, Groom Lake, Nevada State Route 375 (Extraterrestrial Highway), USA:
By definition Area 51 is a conspiracy - It is a top secret military base used for building and testing new military inventions, which apparently operates without any formal congressional oversight.
Secret developments such as the now declassified A-12 OXCART a secret Lockheed Corporation plane are confirmed to have been built and tested in Area 51 [source]. It is claimed that the A-12 OXCART had a wide, disk-like fuselage designed to carry vast quantities of fuel. It had a stealth capability and could travel 2000 miles per hour [source] - pilots flying over Area 51 would presumably have considered the flying machines UFOs at the time.
However modern conspiracy folklore says much much more is going on...
The evidence for it is hard to find as workers at Area 51 have to sign an oath of secrecy. But if any credible evidence appears it will be posted on here in due course...
A brief summary of the conspiracy theories are:
1. The storage, examination, and reverse engineering of crashed alien spacecraft (including the wreckage from the legendary apparent UFO crash at Roswell, New Mexico, 1947)
2. Examination of dead aliens that came in UFOs and interrogation of living aliens
3. Manufacture of aircraft based on alien technology
4. Meetings or joint undertakings with extraterrestrials
5. Development of exotic energy weapons
6. Attempts at weather control
7. Established means of time travel or development of time travel technology
8. Development of unusual and exotic propulsion systems related to the Aurora Aircraft Program (a cutting age spy plane)
Video clip of trail allegedly left by Aurora craft: http://www.youtube.com/watch?v=qpL3_n9RXPM
9. Simulation of moon's environment: Possibly where they filmed a cover up of the Apollo moon landings in 1969+ [Moon - Conspiracy Files - theVoiceofReason.com].