Well I like burgers like chicken burgers, cheeseburgers and things like that with onions and relish or some mayonnaise or special sauce on it. What sort of burgers do you like that are the same as these or similar to these?
I skip the relish and mayonnaise and special sauce, and in addition to the “meats” you mentioned I like various veggie burgers, e.g. black bean burgers. And straight up beef burgers. And there are few things that can’t be improved by the addition of bacon.
I like salmon burgers. I generally eat them pretty simply with just some thousand island dressing.
There are two different questions here.
As far as protein goes, I like beef, but I’ve also had (and enjoyed) burgers with turkey, bison, and ostrich. Up in my home state of Wisconsin, they’ll make burger patties out of bratwurst meat, and those are delicious (I had one last weekend, in fact). And, TVP (texturized vegetable protein, i.e. soy burgers) can be very good. I also like chicken sandwiches, but unless it’s ground chicken meat, I don’t think of it as a “burger.”
For toppings, I’m kind of fussy, and don’t like veggies on my burgers. Cheese (cheddar, Swiss, or American), bacon, and ketchup are my usual; I’ll sometime go with steak sauce, and crispy fried onions.
I like all beef cheeseburgers (American cheese), with lettuce, tomato and onion (sliced or grilled). A little mayo, mustard and ketchup. Occasionally I will add bacon.
I don’t like much else on burgers. No mushrooms, though I like mushrooms. Especially no BBQ sauce, it just doesn’t belong.
My favorite burger is a turkey patty with bacon, American cheese, lettuce, tomato and barbecue sauce. Although I do occasionally eat meat, I find that a beef hamburger is too heavy for me.
I like a rare burger with bleu cheese and onions, but I’ve had to cut way back on meat, so I eat these in fantasy. I, too, love a good salmon burger. I splash them with a dry white wine and season them with garlic and onion just before cooking, then serve them with a dollop of plain yogurt and a sprinkle of fresh dill. Yum.
I was at a place that served their burgers (or veggie burger made out of a pistachio base, it was also quite good) on a pretzel bun and they spread peanut butter on it.
Sounds odd but it what scrumptious! 
Moved to the proper forum
A well-made burger of just about any kind is good with me. I don’t like the far-fetched too-many-toppings type, and I think there are perfectly good foods that don’t belong on a burger.
ETA: Well, they don’t belong on MY burger. You eat what you want. 
Beef. Fatty ground chuck or short rib. Toppings and condiments can vary but nothing but beef is good enough for the meat.
Lamburgers are really good, with a minted yogurt dressing and salad greens
I had some lamb sliders with some kind of mild blue cheese and they were totally amazing. Wish I knew where to get some more.
I really enjoyed a burger I had that had hash browns and a fried egg on it. I can’t remember if there was condiments, maybe a bit of mayo or something on the bread.
I’m good with Beef or Buffalo. I’ve tried black bean burgers but every one I’ve had has been very dry and mealy.
Toppings vary. I like Blue cheese burgers, cheeseburgers with different cheeses, DQ recently had an A1 burger that wasn’t bad. I just can’t do onions (they disagree with my stomach) or some of the odder ingredients.
Buffalo is pretty good. I like a burger with a fried onion ring and A1 sauce, but onions are starting to bother me also. A couple of variations I’ve done, a burger topped with fried clam strips and tartar sauce, or topped with cole slaw and Russian dressing.
There’s no jar in the fridge called “Lithuanian Brushing His Teeth”.
I like to take a pound of steak, trim off all fat, then grind the meat. I divide the meat into quarters and form 4 patties. Atop two of the patties I place spinach and blue cheese, then I top them with the other two patties, sealing the edges.
I dip the burgers in Worcester sauce, salt and pepper, then vacuum seal them. Sous vide rare, then sear with a torch. Serve on a big bun with condiments on the table.
Johnsonville Grillers are pretty good; they’re pork, IIRC.
They are pretty good – they’re similar to the brat patties that I mentioned in my earlier post. And, yes, they’re pork.