I've gotten quite a few odd presents from my Grandmother that make very little sense at all... like a second hand recorder (shot to pieces, was impossible to get a decent sound out of it... the ones I had from primary school over a decade ago were far better) and a second hand country CD (I quite like country like I like having the skin peeled off my hands with a rusty hacksaw)... both of which she was oddly serious about and thought I'd find them useful or something.
A few years ago, I started a tradition among my friends of giving really odd presents to each other. So far we gave to one of our friends (turning 18, never really had a girlfriend before) two books, one called "The Colour of Sex" and "Beginning Fatherhood" which he found peculiar. In return for my birthday he gave me "The First Sex" which is an odd collection of statistics written by what looks to be a feminist writer that is supposed to explain why women are about to take our the entire world.
The oddest present I have given so far though... is 25 meters of bubble wrap to my friend for his 18th birthday. He didn't really know what to do with it... but almost every other one of ours friends, apon seeing it exclaimed "OH! THIS STUFF IS THE GREATEST!!!" and then leaped apon it all.