1) I think the number one importance is good ground beef with a nice, high, fat content. Results in much juicier and tender burger.
2) hand-formed, thick, patties are a must. The production line pre-formed patties are too thin, too dense, and improperly seasoned, if at all
3) Thick wedges of tomatoes, onion(or grilled), and a nice bed of crisp lettuce.
4) Toasted bun with some crunch to it
Get those 4 things right and everything is just a cherry on top. Cheese, mayo, ketchup, mustard are all great, but if the four things above are wrong, then it's simply putting lipstick on a pig.
So, why do so few get it right?
For Southern Californians, the beloved icon In & Out Burgers is classic example of a mediocre product. Paper thin patties with no flavor where buns and condiments end up the being the primary thing you taste in each bite. You have to go off-menu to, at least, the custom "3 by 2" three patty burger to begin tasting meat and it doesn't get real until the "4 by" at which point that's a fairly expensive mediocre burger.
