I kind of like this one. It seems like a cop-out to include something that another person couldn't have, due to uniqueness, such as home videos or mix CDs, though those are the first things that come to mind. As such, these are clearly just my best guesses, and not something I can guarantee. I will be pleasantly surprised to be wrong, though.
A book you own that no one on your friends list does
Wilderness Lost: Religious Origins of the American Mind
A CD you own that no one on your friends list does
We Support Greenpeace, an import/bootleg recording of the solar-powered R.E.M. show, 19 November 1992 at the 40 Watt Club in Athens, Georgia. Listed on CIRUL.
(One track from this show is in the Alternative NRG compilation)
A DVD/VHS tape you own that no one on your friends list does
Our Very First Sex Tape.
A place you've been that no one on your friends list has
Stary Smokovec, Slovakia.