I just read a help page by a mail provider in which they state that all mobile phone numbers will be stored as a salted hash. This strikes me as interesting, since phone numbers don't contain a lot of entropy: about 31 bits by my calculations.
Depending on the hashing function, generating 231 hashes should be quite fast. Adaptive hash functions like bcrypt allow to increase the number of iterations. Cracking such a hash would take considerably longer, but using too many hashing iterations will slow down the application as a whole.
Long story short: is there such a thing as a lowest amount of entropy below which hashing becomes either pointless or harmful?