I have to say they're mostly utility. I have many first editions (as most academic books only have one anyway), some books that the authors gave me. They're not signed, though.

I think this is because of what signing signifies. It's something an author does to honor a reader; it signifies the status of the author, as the signature s a sign of value, and with that, it also signifies the difference in that status between author and reader; it's something the author gives out. But I'm an author myself, I'm a colleague. (and of course in academia books, most readers are colleagues and students; most of our books aren't written for non-academics)

To sign a book for me could actually be construed as an insult, as it wouldn't treat me as a colleague, if that makes sense...