Can I use Cheddar cheese for pizza? I know that most of the time Mozzarella cheese is used for pizza and often in combinations with other cheeses including cheddar. 

I have noticed in quite a few things I cook like sandwiches, quesadillas and such that both mozzarella and cheddar are very stringy when melted which is perfect for a pizza.

So is it possible to use cheddar as the main cheese in pizza instead of mozzarella?
You can use small amounts of cheddar mixed with the other cheeses. But you'd be disappointed in the results if you tried to use it as the main or only cheese on the pizza.

Cheddar cheese doesn't tolerate sustained, high heat as well as some other cheeses. It can scorch, which tastes and smells bad, and/or the fats can separate from the solids as a yellowish oil. The sharper the cheese is, the less well it will tolerate heat.