My wife had an interesting one earlier this week, which is common.
She had shares in a UK company that went into administration in 2011 (and never came out).

Someone called from the US saying that they had a client who wanted to buy up enough shares so that they could gain a conrtolling interest in the company.
"Due to the timescale we can't write to you, so can I have your email address so that I can send you a document to purchase your shares?".

Er, like no.