I do not really have a favorite theorem but one that I like and can remember is The Handshake Theorem from discrete. I liked it because I understood it and it was a very useful theorem to use in the class. No one else has the same favorite theorem.
The Handshake Theorem states: Let G = (V,E) be an undirected graph with e edges. Then
2e = $ \sum_{\v\in V \ }{deg(v)} $
