I quite like collecting fish and frogs, then giving them obscure human names and displaying them around the house. I do this in both TS4 and TS3, although TS3 has more fun ways of obtaining fish through opportunities. My sim fixed the pipes in the city hall and found a lobster in them. I kept it and named it "President."
This isn't a minor hobby, but it's fun for me to have my sims write books since I like coming up with titles and descriptions for the books. Building up a library of custom books in your house is quite fun and a bit of a challenge if you want a large collection. I'm currently planning on building and owning a library in TS3 that is filled with books my sims wrote over a few generations - science, non-fiction, whacky romances, murder mysteries etc. The library will be on a boat, so of course there will be quite a few books on marine biology.