I wouldn't call it an obsession, but I do like maps. As a child I used to enjoy looking at the the "political" maps & loved to try & find really small, obscure countries that no-one had ever heard of, e.g. Andorra, San Marino.
Nowadays I prefer to look at transport maps, such as tube, bus or rail maps. Every so often I have to check the tube map to see if there are any new stations!
I also, as a previous poster said, love to collect textbooks, and my ambition is to collect & complete all the series I used in school as a child. I am pretty far on the way to achieving this now - Amazon is truly amazing!
If as a teen, nearly 30 years ago, anyone had told me I would be able to collect school textbooks that had gone out of print even then with just a few clicks of a mouse, I would never have believed them!
As a child, my weirdest obsession though (and I haven't yet come across anyone else with this one!) was Christmas Grottoes. You know, the decorated fantasy lands where you can go to see Santa Claus in the large department stores (and these days, shopping malls).
Every October I would insist on going to the stores every week & looking to see if they had started building the grotto yet.
I also used to design my own (the shapes, not the decor) and had a whole pad, numbered from 1 upwards, of different designs, which had to be looked at in order. The simplest one was a boring "Santa in his chair' and the most complicated one was a tunnel system several miles long, going over & under itself.
Yes, I was a very strange child!