Pokémon carnivores eat other Pokémon. It's loosely referred to in the anime but not shown since no one wants to see Pokémon getting eaten! (The Pidgeotto Ash eventually catches went after his Caterpie to eat it. Birds like Bug types, of course.) It's more obvious in the games though, from PokéDex entries and such. Miltank in the games are actually used on farms as milk cows. You can actually buy the milk and give it to your Pokémon to restore their HP. Miltank itself has a 'Milk Drink' move to also restore HP...but it's a bit gross to think about it drinking its own milk in combat!

The anime did have a few references to the fact that people eat Pokémon, including Farfetch'd being so rare because it's considered a delicacy (it even carries around a leek, which is common to cook the poor thing with!), to a farm filled with fat flightless Pidgey that were raised as food for people.