According to Snopes.com it is a myth, one promoted by the 1958 Disney film White Wilderness which not only staged a lemming migration on a turntable, but then herded them off a cliff. There was an article in the Washington Post about how nature movies are made a while back that said:
The lemmings that plunge to their deaths in the 1958 Disney documentary “White Wilderness” were hurled ingloriously to their doom by members of the crew, as a Canadian documentary revealed. Palmer writes that Marlin Perkins, host of television’s “Wild Kingdom,” was known to bait animals into combat [..]
Lemmings do migrate in response to population density and other pressures, and can swim, so there are times when some may drown trying to cross water, but they do not commit suicide. According to The Times, the myth was supported by sudden fluctuations in lemming populations, now believed to be caused by the predator-prey cycle.