What are the most widely used communication protocols in industrial robots to get information to and from the peripherals? (cameras, sensors, end effectors, etc.)

PROFIBUS/PROFINET

There are different levels of protocol depending to the application and needs of your traffic on the network.
At DEVICE LEVEL Profibus and Canopen seem to be the most popular in Europe. At PLANT LEVEL many like Modbus, Lon,...
In WIRELESS it seems ZigBee becoming the most popular in Europe.
At ENTERPRISE LEVEL TCP-Industrial

Thanks for the answers!

Here's my 2 cents:
Regarding the discrete automation world (the Process Automation world as well) it's a bit more dependent on your global location.
Europe: Profibus DP & PA, Profinet, CANopen, Interbus, Modbus,AS-i
North America: DeviceNet, Ethernet/IP, Profibus DP,Modbus & FF
Asia: CC-Link, Profibus, DeviceNet

Generally speaking, Profibus has more nodes installed than any other industrial protocol- just due to the fact that Siemens (the largest backer/supporter of Profibus) has a larger presence globally than say Rockwell (largest backer of the CIP network family-Devicenet, Ethernet/IP and ControlNet and strong in NorthAmerica)
I would bet that for Robotics and Motion Control you will see a migration to Profinet IRT (Isochronous Real-Time) a version of Profinet that allows a high degree of determinism, so that the start of a bus cycle is maintained with the highest precision. The start of a bus cycle can deviate up to 1 µs (jitter). IRT is required, for example, for motion control applications (positioning control processes). Kevin of IAI mentioned Ethercat back by Beckoff Automation. Think of it as being an Ethernet version of Interbus (Token-Ring topology). Ethercat is picking up steam in the Semiconductor world where of course robotics are big as well as vsion systems.