General terms:
* Plant-eaters
* Grazers (for animals that eat grass)
* Browsers (for animals that eat leaves and twigs)
* Phytophagous (scientific term)
More specific terms:
* Folivore (eats leaves)
* Frugivore (eats fruit)
* Granivore (eats seeds)
* Nectarivore (eats nectar)
* Herbivorous (adjective)
The best word to use depends on the specific type of herbivore you are describing.