What are the main styles of pizza that are popular in America?

No.

Those are not common pizza toppings in America at all.

In America there are these (rather well known) pizza styles:

Chicago style

Chicago style pizza is a deep-dish pizza that is baked in a thick heavy cornmeal based crust. The toppings are also added in reverse order of a traditional pizza. First the cheese is added, then a pound or more of sausage is added in a dense patty layer, finally it is topped with sauce. You eat it with a fork and knife.

New York style

New York style pizza is wide thin-crust pizza. The crust is made with a very high gluten bread flour and hand-tossed. Some say that it gets a lot of it's flavor from the NYC water. It is typically cut into only 8 slices for a large pie. You fold the piece in half to eat.

New Haven style

New Haven style pizza is a bit lesser known, and originates from New Haven, Connecticut. There it is commonly called "apizza". It is similar to a New York style pizza in that it has a thin crust, but it is always brick oven fired until crispy. You should not be able to fold a New Haven slice of pizza in half without cracking it. It should also be crispy enough to stand up to it's own weight when held by the crust.

In a New Haven pizza a "plain" does not have mozzarella. A plain pizza consists solely of sauce, oregano, and a bit of parmesan and romano grated on top. Mozzarella is considered a separate topping.

They are most known for their white pizzas. These have no tomatoes at all, the "sauce" consists of olive oil, oregano, chopped garlic, and grated parmesan. The most well known is the clam pie which has fresh clams as a topping. It is generally frowned upon to order this with mozarella.

Verace pizza napoletana style

Although this is the original Neapolitan pizza, it has become very popular in the Pacific Northwest (and maybe elsewhere?). There is a certifying organization, which has stringent requirements for the crust ingredients, oven and so forth. The pies are very thin in the interior, with a slightly puffy edge, and are typically lightly charred in spots, which contributes a lot of flavor. Toppings tend to be minimalist.

We call that style of pizza Cognitive Dissonance here in America. Corn anywhere in or near a pizza? That's just crazy talk. In fact, now that i think about it, i can't remember seeing corn in the same room as pizza. (Maybe they're mortal enemies, or alter egos.)

Others have described the various official American pizza styles and provided great links. Here's a more anecdotal list:

• School pizza - this is (or was, before it became illegal to feed children) typically cheese or peperoni or sausage pizza, horrible to pizza mavens but well-received when you're 15. Either cooked in-house or catered by Pizza Hut, which i note is currently promoting the Big Italy Pizza, shaped like a hockey rink, in the traditional Italian fashion. In my experience, pizza prepared in-house must adhere to the following pattern: cheese pizza is round while meat pizza is rectangular, to serve as something of a visual aid for the kids who have trouble identifying toppings.
• Chain delivery pizza - here, we're talking Dominos, Donatos, the aforementioned Pizza Hut, Papa Johns, etc. etc. etc. Your choices are either thick, thin, or hand-tossed, with a wide variety of meats and vegetable toppings (though, oddly enough, no corn), and red or white sauces. They also like to sell bread sticks with your pizza to ensure you have enough carbs to survive (in America, we're dangerously thin, you see). You can choose delivery, pick-up, and sometimes dine-in.
• Local chain pizza - these places offer a slightly-more-robust dining experience, and will often deliver. They have the normal array of toppings, sometimes a green sauce, and often a few specialties, like Caribbean, Mediterranean, Mexican, or what-have-you. Their menus are more varied, and the pizzas are often enjoyed by little league and high school sports teams after a game.
• Actual Restaurant - here you are most likely to unearth something slightly crazy, but usually pretty tasty. They take more chances, mix things up, and turn out fantastic pizza. You can find a thick white cheese monster with Colossal Shrimp, smothered in Garlic butter. Or at Piece in Chicago: Clam & Bacon white pizza. Ian's: Mac & Cheese, Lasagna, ...

In fact, i'd say Ian's pizza menu is borderline insane. Almost freakshow weird. S'mores? BBQ Potato Bacon Ranch? Yeah, they went out of their way to put the nuttiest stuff imaginable on their menus. And this works! Honestly, we Americans love this kind of thinking!

But what is the one thing don't they have? Corn.

Common Toppings in the United States are:

Meat

• Pepperoni
• Ham
• Bacon
• Ground Beef
• Italian Sausage

Vegetables

• Green Bell Peppers
• Red Bell Peppers
• Onions
• Mushrooms
• Black Olives

There are a couple other toppings that are used almost exclusively on a single pizza type

BBQ Chicken Pizza - Chicken with BBQ sauce instead of a tomato based sauce

Hawaiian Pizza - Ham and Pineapple

Of course, one of the great things about pizza is, you can put almost anything on it. Whatever your taste preference is.

Check out this very comprehensive article on Slice that describes the regional pizza styles in America. Each style below links directly to a nice description and picture.

http://slice.seriouseats.com/archives/2008/01/a-list-of-regional-pizza-styles.html

The article lists 21 distinct styles:

• Neapolitan-style pizza
• New York–Neapolitan (aka "Neapolitan-American")
• New York–style
• Sicilian-style pizza
• Grandma-style pizza
• New Haven–style apizza
• Grilled pizza
• Bar-style pizza
• Trenton tomato pies
• Old Forge–style pizza
• Detroit-style pizza
• Deep dish
• Stuffed pizza
• Chicago thin-crust pizza
• Midwest-style pizza
• St. Louis–style pizza
• California-style pizza
• Ohio Vally–style pizza
• New England Greek–style pizza
• D.C. jumbo slices
• Pizza parlor–style pizza

No, there is no such thing. That is just one of those wacky things where folks in one country are doing a sort of caricature of what they think folks in another country eat. Hilarious, but in no way authentic.

There are four pizza toppings or combinations that are the most popular in the US:

• Cheese - nothing but tomato sauce and mozzarella (sometimes a blend of cheeses)
• Pepperoni - add pepperoni to a cheese pizza
• Supreme - many variations, but commonly tomato sauce, mozzarella, pepperoni, loose ground pork sausage (or "Italian" sausage), bell peppers, mushrooms and onions (often black olives)
• all meat - many variations, but often tomato sauce, mozzarella, three or more of: pepperoni, ground beef, loose ground pork sausage (or "Italian" sausage), ham, bacon, Canadian bacon, other "cased" and sliced meats such as salami, etc.

Also popular:

• Veggie: some combination of vegetables with tomato sauce and mozarella
• Hawaiian: ham or Canadian bacon and pineapple with tomato sauce and mozzarella
• Margherita: red tomato sauce, white mozzarella cheese, green basil
• BBQ - barbecue (aka BBQ, Bar-B-Q, etc.) sauce and shredded or diced chicken, pork or beef (usually brisket)
• White - no sauce or sometimes alfredo sauce, mozzarella or another white cheese and spinach
• Many menus list available toppings, crust types, sauce choices and sizes and the customer chooses their own combination

In addition to the other crust styles already mentioned by hobodave, there are quite a few variations mostly of thickness, crispness and chewiness (also variations in added ingredients such as garlic or herbs and even cheese). Some restaurants serve a "Neopolitan" style which may or may not be authentic but frequently the only discernible distinction is that it's rectangular instead of round.

American pizzas typically are covered fairly heavily in toppings in contrast to what I understand to be the case with genuine Italian pizzas.

With the increase in the number of good restaurants, international travel, cooking and travel shows on TV, etc., awareness of and interest in authenticity and variety have increased and many people have ventured outside their familiar territory to try new things.

See also the Wikipedia article Pizza in the United States.

Short version: American pizza has pepperoni, the meat product that's like a really bad hot salami (pepperoni means pepper in Italian). Corn in pizza is weird, but most non-Americans think Americans only eat corn and only drink coke.

Long version: America is a very big country. More than 5x the population of Italy and many more times the size... I lived there for 3 years and I love pizza, so I did some research trying to find what pizza meant there. It means many different things and they have some of the best and worst pizzerias in the world.

Some places with their own style are:

• New York, probably the most famous. I don't think there is a city with more places that selling pizza anywhere in the world. Maybe only 10% of them are good, but some of them are really good. Check slice for names, like DiFara. Which makes the simplest and most amazing pizza I've ever had. In NY they also have a lot of weird toppings, but not on the good places.
• Chicago, with the famous deep pizza and the more classical style (see what the guys from Chicago Pizza Club review). Most common topping is sausage.
• The midwest. They cut the pizza in squares and it's not famous for being good. They also use a lot of sausage.
• New Haven, representing Connecticut and most of New England, it's supposed to be more close to the Italian. The most famous topping are clams.
• California, famous for the weird toppings, see California Pizza Kitchen as an example. They also have classical pizzas that are really good, but none believes them.
• The Pacific Northwest area has a lot of places certified, so I guess is actually the closest one to Italian, but I found a lot of variety in the toppings of the regular places. They pay more attention to the quality, in general.
• Chains. They are everywhere and are terrible and shameless in using any kind of topping. I would believe they shell pizza with corn.

It's often claimed that modern pizza originates from the US Chicago and Detroit area. In Italy it was a simple bread dish with a few flavorings on top, and for poor people. Then in the US it started getting more elaborate toppings; then this got exported to Italy by returning expats, some of whom started businesses offering this US-style, topping heavy pizza. Then demand by American visitors (some say mostly troops during WWII) expecting the local "authentic" pizza to be a refined dish expanded these returnees' businesses and prompted them to refine it to met this demand. This cultural back-and-forth-and-back-again is refered to as the pizza effect sometimes. I think with respects to pizza this has happened several times already, in various ways, and this might be just the latest iteration of this phenomenon.

But most people here in Europe I think know Americans don't eat corn on pizza. There's other pizzas that have corn as a topping, I think it probably refers more to the bell peppers and the hot salami, which is imitating the American "pepperoni" (which is not and actual Italian word, there's a word "peperoni" which means something compeltely different) which is a spicy salami-like meat product and the stereotypical American topping. Corn as spereotypically American might and probably does play a role, but in American pizza chains here don't have corn on pizzas so I think it's not a misunderstanding. I think Americans might not realize people use geographical terms like that as shorthand like that without actually implying that this is an authentic dish from there, I guess here in Europe people we can do that because different countries are more nearby and we actually see what they're like firsthand. While Americans might interpret these things much more literally as might be the case here.

In America we have a pizza called "Chicago Deep Dish", but for the most part everyone wants to be as simple as "Neapolitan."

Being from Ann Arbor, Michigan, I'm also familiar with "Detroit-style" pizza. This is a rectangular pizza cooked in a deep metal pan. The crust is crunchy, chewy, and rather oily, and the toppings go right to the edge, forming a crispy border of browned cheese and sauce against the rim of the pan. Toppings are placed under the cheese, and sauce on top.