Really you shouldn't have burgers rare...you can get food poisoning quite easily. this is because the meat in a burger is a piece of meat that was minced, so the outside surface of that piece has been minced and is now not only on the outside of the burger but on the inside...and if uncooked can lead to food poisoning. Taht's why rare steak is ok...germs are on the outside only and you cook those away.
My burgers are similar to everyone else's:
minced meat, mixed with some mustard, worcestershire sauce, salt and pepper, then fried in a little butter. place inside roll of choice and add a slice of tomato, onion, and some cheese, melt under grill, eat!