Agents possess extraordinary powers to manipulate their surroundings (including superhuman strength and the ability to flawlessly dodge incoming bullets). However, Agents still have limitations, being "based in a world that is built on rules". Thus, they cannot fly (at least except Smith in the final fight against Neo), walk through walls, or perform any other actions outside the boundaries of their programming. They are programmed to keep order within the system by terminating troublesome programs and human avatars which would otherwise bring instability to the simulated reality.
Agents have the ability to take over the simulated body of any human that is a part of the Matrix, converting it into a copy of their own. If that body is killed, or an Agent needs to change its location quickly, it can assume the shell of any other human hard-wired to the Matrix in a matter of seconds. Agents also have the ability to communicate with each other instantaneously, represented via their earpieces (thus, when Agent Smith once removed his earpiece, he briefly severed his link with the other Agents).