Uses for gate expressions, Nor and Xor
There is one special thing about the NOR gate. It (along with NAND) is what is called universal gates. That is, any other gate (AND, OR, NOT, etc.) can be implemented using just NOR gates. I think this picture shows why:



So, as far application is concerned this is the main thing. For Ex-OR, it is commonly used as a state toggle or a buffer. If you look at X-OR truth table:



You will see that if I set one input to zero it acts as a buffer. If my input is 0, then output is 0 and if my input is 1 the output is also 1 (buffer - output same as input). 

On the other hand if I set one of my inputs to 1, then it acts as a toggle. If my input is 1, I get 0 and if my input is 0 my output is 1. 

Why are buffers used? In digital circuits it is primarily used to introduce some time delay. Toggling - well though NOT gate does the same, it is advantageous to use X-Or because by just changing the first input 1/0 (Toggle/Buffer) can be achieved.