The instability that led to the War of Five Kings was caused by three things:
1) The plots of Varys, a loyalist of House Targaryen.
2) The plots of Petyr Baelish, whose motives are somewhat unclear, beyond personal advancement.
3) Cersei and Jaime's secret relationship (which both 1 and 2 exploit).
Joffrey's succession only caused a problem because he was not, in fact, the rightful heir to the throne. Without that, neither Ned nor Stannis would have opposed his taking the throne, it's rather hard to imagine that Renly would have fancied his odds, and Balon Greyjoy's insurrection would almost certainly not have happened (or else, been easily put down like the previous one) in light of the unity of the realm.
When you think about it that way, Cersei (and Jaime) completely screwed over their House's long-term prospects.
Tyrion thinks that too, in Clash of Kings I believe. All Cersei had to do was have one child by Robert and her family would have had an undisputed claim on the Iron Throne.