Here is a collection of some of the most well known unsolved mysteries (links to Wikipedia). They make for good reading on a rainy day.
Wow! Signal – Possibly extraterrestrial signal caught by SETI on August 15, 1977
Valentich Disappearance – Disappeared without a trace in a Cessna October 21, 1978 after reporting that he encountered a strange flying object
The Lost Colony – 16th century colony where all the inhabitants disappeared
Mary Celeste – Brigantine ghost ship discovered outside the strait of Gibraltar in December, 1872
Felix Moncla – USAF pilot that disappeared while pursuing an unidentified flying object in 1953
Ararat Anomaly – Unidentified object visible via satellite and aerial reconnaissance in a hard to reach location on mount Ararat
Oak Island – Location of a strange pit that many believe contain a hidden treasure