I collect goldfish- pretty much any goldfish- in memory of some very personable pets, as I no longer have room/money for big tanks. As money allows, I want other fish also- I love finding examples of species I've kept (such as many of the cichlids), and freshwater 'pet' species in general. I'll get any fish that appeals though, if I can.
Other than that, I collect dinosaurs/prehistoric reptiles and fish (shared with my daughter); dragons (okay fantasy not real) that I like, and pieces that speak to me. Oh, and certain Arabian horses to give my mother- she used to raise them.
Brand and age don't matter to me. Even pieces in rough shape that appeal can possible be restored to glory. And I would kind of like to do some of the inverts.