I'm a cheese whore. I love cheeses of just about any type. I would have to say the best cheese on a burger is blue cheese. A good creamy Gorgonzola can't be beat in my book.
Shredded xtra sharp cheddar on top of a chilli on top of a sunny side up fried egg on top of bacon on top of diced onions on top of a 1/2 lb of 75 -25 beef pork mix burger.
That certainly sounds awesome!