When you are checking a conjecture or working through a proof, it is nice to have a collection of examples on hand.

There are many convenient examples of commutative rings, both finite and infinite, and there are many convenient examples of infinite non-commutative rings. But I don't have a good collection of finite non-commutative rings to think about. I usually just think of a matrix ring over a finite field.

Do YOU have other examples that you particularly like/find easy to use/find to be a good source of counterexamples?