I can talk about the Thirty Years War (1618-48), arguably the apogee of the mercenary and the last great conflict fought using them.

The War itself is a vast and extremely complicated mix of religion, politics and personalities, but it is best remembered as possibly the most destructive war in European history. Up to a quarter of the population of central Europe was killed, a result of battle, disease, famine and mercenary action.

Because the war was so long and so huge in scope, the developing states of the early modern period simply did not have enough resources (tax revenue, food, arms etc) to raise and sustain armies in the numbers they required. To solve this they turned to private individuals, who would raise the armies themselves and sustain them simply by seizing the resources they needed from the local population of wherever they happened to be stationed with state approval. These seizures were known euphemistically as 'contributions', and would be levied in the form of quotas imposed on towns or districts in which the armies were stationed. The most famous private contractor was Wallenstein, who became director of the entire Habsburg war effort until his murder by the connivance of the emperor.

Naturally, this caused huge outrage and suffering; whole areas of Germany effectively became wasteland as passing armies picked them clean. This backlash coincided with development of the resources of the state in the mid and late 17th century. Governments recognised that the use of mercenaries was not ideal; they were often unreliable in battle and could act with greater impunity outside the direction of the central government making them harder to control than government-led troops. There was also fear that mercenaries could threaten the government themselves, as Wallenstein had been accused of doing.

After the Thirty Years War, therefore, states tried to focus on raising armies through their own resources- they slowly developed institutions of administration, taxation and military supply which would make large-scale use of mercenaries obsolete. By the time of the great coalition wars of the end of the 17th century, this had been largely achieved- the state could generally afford to raise its troops itself.

Hope this goes a little way in answering your question!