There has been a few topics like this one and there has been no reports of a limit, just as long as you have children to take over the next generation and keep backups just in case something does go wrong.

Sometimes families will disappear off of one of the 5 game slots, if this does happen don't make a new one over it unless you want to start over because there's always a way to retrieve it through the game's automatic backup saving.
The longest generation I've heard of so far is generation 20.