This is all opinion. Be nice.
I'd like to offer a voice of dissent here: I like American Cheese, and not only the really good, freshly sliced deli variety. I like the stuff that comes individually wrapped in plastic, too. You know when Homer said "mmm. Sixty-four slices of American cheese" and proceeds to eat them all? Yeah. That was me and I wasn't laughing.
So what is it? Why is this stuff so good to me? Why do I have American cheese cravings? I'll admit that a big part of it is nostalgia - I grew up eating cheese and mayo on good deli rye as an afternoon snack. It's an independant cheese; I can't think of another cheese readily available in the United States that I'd eat all by itself between two pieces of bread (ok, except Brie, but that's not quite so standard). Other cheeses just feel like toppings.
Speaking of toppings: I like the way it melts and I like the way it tastes melted, particularly on six ounces of grilled beef. Swiss isn't bold enough. Cheddar is too sharp and oily. Mozzarella is too soft. Blue Cheese is too salty. Monterey Jack is too...south-western. I love all of these cheeses in different contexts but on a burger they pale in comparison. Maybe it's because its relatives live in a can, but no other cheese melts as well.
It sounds like I'm saying American's good because it's inoffensive, but that's not it at all. It's that even after all this time and all these cheeses, American cheese still confuses me at some fundamental level. I want it to taste like something else, I want to be able to associate it with cheddar but I can't, not really. It's like the black sheep of the dairy world, the cheese-fairy reject. But that's alright; I still like the look I get when I order american and mayo on a roll.