To me, there were two major conditions that allowed the revolutions in the Latin American countries to occur. One condition had to do with things that were internal to the countries, the other had to do with Europe.
Internally, the major issue was the discrimination faced by the creoles. They were ethnic Spaniards who were born in the colonies. They felt they were as good as the Peninsulares but they were excluded from important offices and positions.
The other issue was the weakening of the Spanish monarchy. This came to a peak in the early 1800s when the Spanish monarchy was actually overthrown by Napoleon. This caused some amount of chaos and a severe decrease in the loyalty felt by the colonists towards Spain.