Meant to do this...well, whenever it was the question of the day, basically, and never got round to it.
But anyway. I guess my main collection is my Doctor Who DVD, VHS and CD collection. I haven't got everything - on first release of the VHS there were a few stories I didn't get hold of, and until they come out on DVD won't have (hello, The Sunmakers and The Android Invasion, for a start...), but I've got all the CDs of the missing episodes, and buy each DVD when it comes out (still haven't got Mannequin Mania yet, though. Will order that when I get paid on Friday.
What made me start the collection? Well, I'm a fan of Doctor Who, so I like to have the DVDs so that I can watch episodes when I feel like it. I occasionally go through phases of starting to watch the series from the beginning, and get part way through serial B before giving up. One day, though..!
I have other collections - books in general, including Doctor Who again (novelisations, NAs, MAs, EDAs, PDAs, and a few of the NSAs), my Dalek collection (in theory, every Character Options Dalek, in practice depends on when I can afford to buy a new one), Pet Shop Boys records (including a few rare items)... But yeah, the Doctor Who one is the main one.