What is the age limit for radiocarbon dating of fossils?

The age limits for radiocarbon dating anything is about 100-40,000 years.

However, to date the early hominid fossils that have been found in Africa scientists have used Argon/Argon dating to date the volcanic lava and ash it was buried between. The age limits of Argon/Argon dating are 1,000 to the oldest rocks on earth.

Generally, you never really date the item of interest when figuring out the age. You will date items that it was used with, buried with, cooked with, etc. Many different dating methods are used to date the items and the age limits vary between each method.