Lemmings do not commit mass suicide by stampeding over a cliff into the sea. This legend acquired legs in 1958, when Disney released a film called White Wilderness. The director imported some lemmings which had been captured by Inuit children, drove them off of a cliff (the lemmings, that is), and used trick photography to vastly increase their numbers in the movie. According to the film, the lemmings were not intentionally committing suicide, but merely died from exhaustion and drowning in a futile attempt to swim to the opposite shore of the ocean.
However, as revealed by Snopes, these much-maligned mammals do not hurl themselves by droves into the water for any reason, although a few may fall in accidentally.
Lemmings do have large fluctuations in numbers, but so do many wild animals. Lemmings handle the problem of overpopulation through the more traditional means of starvation, epidemics, being eaten by predators (including other lemmings), and migration.