Depending upon your region and the time of year, many of the following peppers can be found at your local grocer or specialty store.

Jalapeño: Green to red, tapered and about 3.5 inches long. The
main hot pepper in Mexico, also popular in the U.S.
Jalapeño Video

Habaneros: Orange, about 2 inches. Among the hottest peppers in
the world.
Habaneros Video

Scotch bonnet: May be red, orange or yellow, about 2 inches. Cousin to habaneros, popular in the Caribbean. Often used in ceviche or hot sauces.
Mariachi (Sante Fe type): Golden yellow to red, conical and about
3.5 inches long. Often stuffed with shrimp and grilled.

Pasilla: Dark green to chocolate, long and thin and about 10 inches
long.
Pasilla Video
Cherry Peppers: May be hot or sweet. Green to red, globular and about 2 inches long.

Asian Cayenne: Green to red, wrinkled and long, about 4-5 inches long. Cayenne peppers are often used in Thai food, and are good for sauces, processing and color extraction.

Anaheim: Light green to red, flat and smooth, about 8 inches long. Most widely grown in the U.S. Found in cans – roasted, peeled, diced and canned. Makes a nice chili.

Ancho: Dark green to red, flattened and tapers to a point, about
5-6 inches long.
Ancho Video

Serrano: Green to red, bullet shaped, about 3 inches long. Often fried and eaten with tacos.

Guajillo: Green to red, flat and about 6 inches long. Good for drying.

Fresno: Green to red, triangular, nice flavor, about 3 inches long.
Fresno Video

Banana: May be hot or sweet. Yellow to red, smooth tapered, about 8 inches long. Used fresh or for pickling.