When it comes to good old American beef burgers, I'm kind of a "less is more" guy. I like to start with beef with an 80/20 meat to fat ratio (ground chuck and brisket), season it simply, and grill it masterfully. My current standard of excellence is the "Paul Newman Burger" served at the Dressing Room in Westport, CT. (For more, see Planet Barbecue, pg. 307: you'll also find my 20 tips for a perfect burger.)
But I also love lamb burgers, Kobe-style beef sliders, veal and beef burgers, tuna burgers, turkey burgers...the list goes on.