The answer to this question varies widely based on what wars for independence you are talking about.
The two greatest sets of wars for independence in the 19th century were the Latin American wars for independence and the American Revolution. These had very different consequences.
In North America, the main consequence was the creation of a democratic form of government that has remained stable. This revolution changed its society permanently, even if some of the change was gradual. It moved the United States away from a class-based, monarchical system to a democratic and egalitarian system.
By contrast, the Latin American wars for independence were much less revolutionary in their impacts. The societies of Latin America remained very much stratified with a small European elite ruling over mestizo and Indian majorities. The governments of Latin America's newly independent countries were not very democratic or stable.
Thus, these two sets of rebellions had very different consequences outside of the fact that both created newly independent nations.