I have looked at Serebii, Bulbapedia, IGN and others but they disagree and often appear incomplete. I am compiling some test data so I can provide evidence for the my eventual answer/to add to the chosen answer.
A simple way to put it, you can obtain stones, selling items, medicine, and feathers. These items include: Leaf Stone, Fire Stone, Water Stone, Dawn Stone, Shiny Stone, Dusk Stone, Sun Stone, Moon Stone, PP Up(?), PP Max(?), Any type of feather, Hard Stone, Star Dust, Fresh Water, Lemonade, Soda, and MooMoo Milk(?).
I went to all of the big sites and checked the lists. The ones with (?) are ones that did not appear on one or more sites, but were still on one of them.