I know that planetary spin can decay over time -- a great deal of time -- and moons are subject to strong gravitational influences from their host planet that makes them a different case... but I didn't want to get too long-winded on this subject.
It's anybody's guess if humanity will still be around when the Earth stops spinning; we may have moved off or died out long before that happens. Our sun will eventually lose enough mass that it will start expanding and consume the Earth, but I'm not going to worry about something several billion years off.
If the Earth stopped spinning right now, we'd be doomed. The sun-side would become an infernal wasteland; the dark-side would become a frozen wasteland; with only the "twilight" border between the two left as habitable... and that would be plagued with terrible weather effects as the hot atmosphere, saturated with large amounts of evaporated water from the boiling oceans, encountered the cold atmosphere. Well, perhaps not doomed... but driven into a subterranean existence.
Edited by - Crash-Drive on 24-03-2003 10:30:08