I think you've all got most of mine - and given me plenty of reading material!
A couple I'd like to know -
What happened to Federico Lorca? He was a Spanish poet and playwright who is assumed to have been executed at the start of the Spanish civil war, but his body has never been found.
What really happened to the Russian royal family? I know that all their remains have now been found, but there was clearly enough doubt and uncertainty over their deaths to inspire stories of Anastasia having survived. We studied the Russian revolution in secondary school (admittedly a while ago) and I remember there were several conflicting accounts of the events.
And my personal favourite mystery - what is the Black Shuck? http://en.wikipedia.org/wiki/Black_Shuck
This is fairly local to my parents and where I grew up, and is nearly always mentioned in those 'local mystery' books you find in small town bookshops. I'd just love to know what it was, and what really happened in Bungay church!