A poster looking for the classic American burger in the SF Bay Area (no fois gras, please) asked the question in the title and continued ...
"One of us said it was all about the meat and the condiments; the other one of believes that the most important part of the burger (after the perfectly cooked meat) is the bun."
My own opinion is the bun is a major player. I enjoy a nice condiment bar with a burger ... however that is just the icing (so to speak) on the burger ... a bonus ... a good burger with the perfect bun is all that is needed. Good condiments have never brought be back to a place ... a bad bun will ruin the whole experience and it is unlikely I'll be back.
The bun can't be stale. It can't be too much bread to burger ratio. It can't be too flimsy to hold up to the burger. It can't be ... creative.
One of the few horrors of moving to San Francisco was the burger served on a sourdough roll. No. It is too chewy. Also, a burger ain't health food ... forgetabout a whole wheat bun.
Though ... I'm starting to think the ciabatta might not be a bad thing. There's a certain synergy with the burger. Uh ... the name that dare not be mentioned ... but I like Jack in the Box's ciabatta burgers. And two burger joints at the top of my list in the Bay Area have an excellent ciabatta buns (same bakery). It holds up nicely to juicy burgers and those with lots of condiments with the bread complimenting the burger taste.