Perceptron learning rate
I agree with Dawny33, choosing learning rate only scales w.

While training of Perceptron we are trying to determine minima and choosing of learning rate helps us determine how fast we can reach that minima. If we choose larger value of learning rate then we might overshoot that minima and smaller values of learning rate might take long time for convergence.

It is okay in case of Perceptron to neglect learning rate because Perceptron algorithm guarantees to find a solution (if one exists) in an upperbound number of steps, in other implementations it is not the case so learning rate becomes a necessity in them. 

It might be useful in Perceptron algorithm to have learning rate but it's not a necessity.