Pokémon seem to eat just about anything. Human food, Pokémon food... They also eat Pokepuffs, but I guess you're not supposed to just feed them those.

[at least, Veronica hoped not. Hmm. Pausing ever so briefly, she hoped that her Sylveon wasn't getting fat off the veritable truckload of pastries she was eating.]

I think they sell some healthier stuff in the stores.