Regional Dishes from the US:
Clam Chowder (New England) - type of thick clam stew
Maryland Crab Cakes (Maryland) - fried cakes with crab meat
Succotash (East coast) - type of bean/corn mash with other ingredients
Collard Greens (South) - a green, leafy vegetable reduced with pork, vinegar and other ingredients
Gumbo (Louisiana) - A stew made with okra and a type of meat (chicken, shrimp, etc.)
Michigan (Upstate New York) - a hot dog with a semi-spicy meat sauce (not chili), normally served with vinegar and chopped onions.
Chili (Southwest, Texas, Midwest) - a spicy bean and meat stew with onions, oregano, cumin, and other spices (not to be confused with chili pepper, though they are incorporated)
Barbecue/BBQ (Southeast, South, Texas, Midwest) - a style of preparing meats such as chicken, beef, or pork with a specific sauce over an open flame. Also, the name for the sauce, which, depending on region, ranges in its ingredients, producing something sweet, tangy or savory.
Chimichanga (Arizona, New Mexico) - a fried burrito with meat, beans and/or cheese.
Keep in mind that immigrant palats have greatly changed the diet of the US, so it's difficult to draw the line between "American" and imported foods. The list I gave above does not include one type of food that hasn't had some influence from another culture (succotash is a native dish, gumbo has West African influence, etc.). Obviously pizza (Italian), sausages - such as hot dogs (Northern European) and tacos (Mexican) are all from different cultures originally, but they've had a lot of time to become "Americanized" and therefore may be included on this list. I've had pizza in Naples, it's nothing like Chicago- or New York-style. And tacos in Sonora are much different than their north-of-the-border cousins.
Some slang terms for to eat:
"to grub" - to satisfy an urge to eat
"to chow" - to eat hardily
"to scarf down" - to eat quickly
"to woof up" - to eat quickly
"to pig out" - implies gluttonous eating
"to snack" - to have something between meals