They did, but not successfully - a quick glance at http://en.wikipedia.org/wiki/Slave_rebellion#North_America will give you a hefty list of failed slave uprisings to consider.

After the Turner Rebellion of 1831, for example, Virginia almost abolished slavery to prevent further uprisings, but decided to maintain it after a close vote.

Slave uprisings such as the Turner Rebellion posed a serious threat to the entire economies and way of life in the Southern states, so were responded to harshly and with massive force.

Punishments for slaves were very brutal, and often involved whipping, rape, mutilation (such as cutting off one ear, or both), castration for males, or execution, by various means such as hanging or burning at the stake.

To serve as a reminder to other slaves, the head of the deceased slave might then be severed and placed on a stake somewhere everybody could see.

As for where slaves could go if they were successful in escaping, during the colonial era, slaves could escape to Spanish Florida, where "Officials at St. Augustine - whose black population was drawn from Spain, Cuba, Hispaniola, and New Spain - celebrated the fugitives' choice of religion and offered sanctuary. They also valued the creoles' knowledge of the countryside, their ability to converse with English, Spanish, and Indians, and their willingness to strike back at their enslavers. Under the Spanish flag, former Carolina slaves raided English settlements at Port Royal and Edisto and liberated even more of their number. As part of the black militia, they, along with other fugitives from Carolina, fought against the English in the Tuscarora and Yamasee wars".

Sources: Suspect Relations: Sex, Race, and Resistance in Colonial North Carolina by Kirsten Fischer

"From Creole to African: Atlantic Creoles and the Origins of African- American Society in Mainland North America" by Ira Berlin