OK, I'm a thread killer when it comes to pizza, but I manage a national pizza trade magazine and trade show (both the country's oldest!), so I can weigh in here. What the others have said is right on the money for Chicago (usually deep-dish, like a pie with dual crusts) and NY (large slices, able to be folded, sometimes baked in a coal-fired oven, which are no longer allowed to be built -- if you visit a place that still uses it, it's be grandfathered in).
For Chicago-style 'za, you'll find Giordano's, Connie's, Pizzeria Uno and DUE and Gino's East among the most popular. In NYC, there's tons of good places (even the Sbarros seem to be better), but Long Island has awesome 'za. Some of the most esteemed places are now running on legend and history rather than good food. Totonno's, Lombardi's, John's, Patsy's L & B Spumoni Gardens are all classics. Expect long lines and lots of tourists. Hole-in-the-wall/ off beat places are often fun finds, too: Pinch–Pizza by the Inch, Slice (a vegan place), Sullivan Street Bakery.
We're seeing a big trend toward gourmet toppings/ sauces now (pesto sauce, sun-dried tomatoes, chicken, Asian influences, etc.), different cheeses (like Asiago, provolone, gorgonzola, etc. blended with traditional mozzarella). Most California-style pizzas fall into this category (think California Pizza Kitchen -- they started the Californian influence). California-style is often considered healthier (zpizza is becoming a big franchise to watch).
"Grandma pizza" and Sicilian-style thick crust are usually cut into squares. There's a big debate here in the office about the way 'za is cut -- our publisher, who hails from Long Island, gets irate if somebody cuts a round pizza into squares (which we do just to tick him off!.)
St. Louis lays claim to it's own style of pizza (although it's often discounted in the industry), which uses a special cheese called Provel instead of traditional mozzarella, and often lots of oregano with a sweeter sauce. It's often cut into squares, although the pizza is round. Imo's is a biggie in St. Louis.
Columbus, Ohio, is also garnering attention for it's pizza scene...
The winner of the 2006 Pizza Festiva! contest at the International Pizza Expo was Mama Mimi's Take-N-Bake, which was a big shocker since it wasn't a traditional sit-down pizzeria or delivery place. Really brought some validity to take-and-bake as a pizza option. For the record, I really like Papa Murphy's, although Tony Boombozz in Louisville (a two-time Festiva winner) and a little place called Mario's in Albuquerque, NM, of all places, are awesome, too.