We all know that Pikmin takes place on Earth; even though we never see any people, the player encounters plenty of man-made objects. It is assumed that humans are long gone, extinct for whatever reason.
In fact, it's been said that Shigeru Miyamoto proposed this very idea himself, though no one can seem to verify the statement and find a source.
At any rate, the next question is when the games take place. And apparently, "Pikmin 3" contains the definitive answer.