On the discussion of Polish Sausage above, I'm surprised there's no mention of grilled onions, the natural accompaniment. Thin-sliced and nearly caramelized, they're a great foil for the spicier sausage, mustard and peppers (while upping the grease quotient).
I'll take a crack at the Pizzas: There are two Chicago Deep Dish styles, with variants.
A "Pan" pizza, as originated by Ike Sewell at Uno's, with derivatives at Lou Malnati's, Gino's East, and others, has a thick, crunchy crust that often contains cornmeal, cheese placed right on the crust, and chopped tomatoes (or sauce), and toppings at the top. But what truly makes it Chicago is sausage: slighly spicy Italian sausage spread nearly as a full layer on top of the pie by some places. Unlike most of the rest of the country, pepperoni is not king here. You won't get mocked for ordering it, like you would for putting ketchup on your hot dog, but you're missing out.
The other style of Chicago deep dish is "Stuffed", popularized by Edwardo's, Giordano's, Nancy's, Bacino's and others. A thin crust in a deep pan, followed by cheese and toppings (which can be as unusual as spinach souffle, prompting some to call this "macho quiche"), followed by another crust and a sauce (usually smoother than the pan-style chopped tomatoes).
But don't be fooled by "thick-crust" pizza. Most pizza places offer a thick crust or "Sicilian" pizza, which is merely more, bready crust. A good way to feed college students, but not a Chicago-style pizza.
What is patriotism, but the love of good things we ate in our childhood?
-- Lin Yutang