For small digital media (e.g., music), I don't really worry about it, since storage space is pretty cheap.
For larger digital media (e.g., movies/tv shows that I download in HD), I don't usually download until I actually am about to watch. For movies, I keep a list on letterboxd of stuff I want to watch. It's pretty big, so sometimes I use an RNG to randomly select something off the list.
For physical objects, my book collection is taking over my apartment. I've tried to make a rule that I have to read a certain number of books before getting new ones, and I periodically sell some of the books that I already read. Still, it's really hard to keep from getting more used books!