The bushy, branching extensions of a neuron that receive messages and conduct impulses toward the cell body are called?

Dendrite- the bushy, branching extensions of a neuron that receive messages and conduct impulses toward the cell body/ Axon- the extension of a neuron, ending in branching terminal fibers, through which messages pass to other neurons of to muscles or glands. hope this helps you  :P 

These are called the "dendrites" I believe.