There have been plenty of rebellions and wars in the past, but the rivalries between various houses usually mean that they never get very big. The Targaryens were special not only in that they had dragons but that they were in some ways above the fray when it came to the squabbles of the lesser houses. No one wanted any other house but their own to rule, buy the Targaryens weren't as bad because they were already in charge.
This is an important factor. Having a Targaryan king meant that the other great houses such as the Starks, Lannisters, Baratheons, Martells, etc. were all equal. Like Varys says in ACoK, power exists where people believe it exists. As long as the Targaryans held the Iron Throne, they were in charge, dragons or no.
Once Robert rebelled, he upset that balance. Suddenly the great houses were not equal, the Baratheons became the royal family by conquest. Fourteen years was not enough time to establish their rule as a precedent. Why should Joffrey (even if he was Robert's son) rule? Why not Stannis or Renly? Why not Robb Stark or Balon Greyjoy? Once the Targaryans are out of the picture it becomes a free-for-all.