What's with the new trend towards an "open hamburger"? You'll see it particularly at upmarket places, like Milk and Honey. The whole point of a hamburger is that its contents are surrounded by bun, you can pick it up and eat it without diving for a knife and fork.
According to Miriam-Webster, a hamburger is:
a sandwich consisting of a patty of hamburger in a split (typically round) bun
On another note, here's the hamburger I made last night. Jalapeños and sour cream on hamburgers is truly divine. Garnished with Bacon, of course.