This may be a touchy subject. You see, I'm from New York, and New Yorkers have strong opinions about pizza. Granted, I'm not from New York, New York, but my relatives are. So I have the bias from childhood that NYC pizza is the best there could ever be.
That being said, there's nothing wrong with a little variety, and outside of New York and Chicago, Connecticut may boast of its own excellent pies. This fine reputation comes primarily from the New Haven style, made famous by Frank Pepe's. Legend has it that New Haven is the birthplace of American pizza. New Haven style apizza is thin, crispy crust baked in a coal oven, sometimes until the crust is black. Usually there's a variety of gourmet toppings, but the plain version is just tomato sauce, basil, and pecorino romano cheese. Pepe's other speciality is the white clam pie, with olive oil, garlic, and clams. Very different from New York style, which has lots of mozzarella cheese. In some ways, New Haven pizza is more similar to the pizza I had in Naples, where they eat it with a knife and fork.
Although Pepe's is the most well known, there are tons of great pizzerias all over the state. I'm only listing a few of my personal favorites here:
Frank Pepe's Pizza Napoletana, New Haven: http://www.pepespizzeria.com/
Why go here? It's a historic CT classic.
Best dish: White clam
If you're in the area, also try: Sally's Apizza, Modern Apizza
Willington Pizza House, Willington: http://www.willingtonpizza.com/
Why go here? For the thick crust, homemade red sauce, and most of all the generous array of toppings, from eggplant to capers to canadian bacon. The atmosphere is cozy and old fashioned: the restaurant is a 250 year old farmhouse and historic memorabilia and antiques line the walls.
Best dish: Go for one of the speciality pizzas, which range from the traditional (Greek pizza) to the more creative (such as the red potato, with sour cream, red potatoes, chives, bacon, and cheddar cheese). My favorite is the House Special (hamburg, sausage, green peppers, onions, mushrooms, and pepperoni).
If you're in the area, also try: Randy's Wooster Street Pizza (UConn, Storrs). It's New Haven style, but with some truly unique and bizarre topping combinations. My favorites are the Napolitana and California pizzas, but if you're feeling adventurous, try Skippy's Dare (bacon, provolone, and peanut butter with a white sauce).
Harry's Pizza, West Hartford: www.harryspizza.net/
Why go here? The pizza is as simple, fresh, and authentic as it gets. It's the real deal. The West Hartford Center branch looks like a typical pizza parlor, with plain wooden booths. There's another branch in Bishop's Corner, but I haven't been there.
Best dish: Tomato Basil or True Napoletana.
If you're in the area, also try: Luna Pizza (trendy and upscale, with plenty of outdoor seating, right next door to Harry's).
Yanni's Pizza Restaurant, Newington: www.yannispizzarestaurant.com/
Why go here? Because it's more than just pizza! The pizza is obviously fantastic, but their other dishes are great as well. This is a true family restaurant, and a popular one (the line was out the door when we got there and we had to wait at least 45 minutes for a table). It was worth it. They have Greek specialties, calzones, grinders, all at reasonable, affordable prices.
Best dish: Eggplant grinder
If you're in the area, also try: Andy's Italian Kitchen (Farmington).
What style pizza is best? Which pizzeria in Connecticut is best? I'm not going to go near these questions, but feel free to go at it in the comments!