Interesting topic.
I don't have anything that I tend to collect on an absolutely must have them basis, but I do have a fondness statues of fantasy or mythological creatures, particularly dragons.
Back in the 90's there was a monthly magazine collection called beasts and beings. These involved fantasy characters one coming each week, they are made of resin and range in size from a couple of inches (for the lepricorn and elf), to about six inches high for creatures like the ogre and the cyclops. these run the gammet from a ghoul, vampire and zombie, to a dryad wizard and even cerberus.
In addition to the beasts and beings collection I have a number of other fantasy statues, for example, my lady bought me an absolutely beautiful and very delicate plaster work phoenix (which had to be ordered from Russia), which is currently sitting ontop of my bookshelf along with a paper work chinese dragon, she also bought me a very detailed and beautiful ceramic mermaid statue.
I have a number of dragons, from a small blue one made of resin sitting ontop of a christal ball, to a lnong fluffy winged serpent who lies along the back of my sofa, to two very ornate dragons who sit either side of my fountain.
Though I do not collect them, I also have a number of carved chess sets, including a chess set of the Lotr film characters which again was bought in installments, to a very lovely brass chess set of king Darius of persia and Alexander the great which I bought in griece, indeed when I go travelling I like to bring back something or other special, to add to my collection, so I have a small alabaster pyramid and a replica of Tutankhamen's death mask in marble that I bought in Egypt, as well as a replica of the Statue of liberty that of course came from New-York.
Most statues are abstract rather than being specific characters from fantasy series, but I do have one or two pieces, such as an official Harry potter wand (probably quite valuable now).
What is even more complicated, is that my lady collects angel statues, indeed we've recently been sent a few of her things from Germany including that collection.
So, well yes, we do have quite the number of strange things around our house, but hay that's what makes the place interesting .
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)