I think pack rat is a collector of various miscellaneous stuff, maybe like newspapers, tool parts, stuff you do not really need but want to keep.
Hoarder would be keeping anything that you may have use of in the future. Although a Pet Hoarder is pretty scary. and messy...
Anyways, I shall answer my own question now.
My first collection is simply foreign coins, they just simply collected in a box and I had a pretty impressive collection (and some pretty old coins) until one day someone broke into my room and stole all of it. The collection was never recovered and I am now recollecting again.
As for a collection of anything I am a fan of, I have a pretty decent Panzer Dragoon Collection. Having almost all of the music cd's, books, and of course the games it self. I was very lucky to get a pewter statue that I had only seen on e-bay once three years ago. There is still more I want to collect but they are on sale for outrageous prices.
Lastly, the largest collection of all here is books. There are three large shelves full of books and at least one half the size. All are pretty much full and the bulk of the books is mainly history, reference, fiction and various Japanese books.