Korean food: These are my favorite, and probably more popular things you'll find at any good Korean place.
Appetizers -
Favorites are dumplings (mondu), light pancakes filled with either veggies (pajon), kimchee (kimchee pajon), or seafood (haemul pajon). I also like squid (oh-jing-a) Depending on the restaurant, there will be others, but everyone korean place has these staples.
Mondu -
Pajon -
O-jing-a
Meat BBQ - Note: The term "BBQ" is used wrongly here, since BBQ denotes cooking with smoke. Korean BBQ denotes usually raw meats brought to the table and cooked on a small hot grill placed in the middle of the table. The diners control the cooking.
Bulgogi - Slivers of beef marinaded in sweet garlic soy sauce
Kalbi - Short ribs marinaded in sweet garlic soy sauce
Daeji-gogi (or daeji bulgogi) - marinaded pork, usually spicy
Dak-gogi (or dak-bulgogi) - chicken, which may or may not be marinaded
Bulgogi -
Kalbi -
Daeji -
There will probably be other assorted meats, including plain unmarinaded versions of the above.
Hotpots or Soups
Jam-bong - hot and spicy soup with (hopefully) lots of seafood and vegetables. Noodles as well. Seafood can vary including squid, shrimp, clams, mussels, or fish.
Udon - Noodles in mild soup. Specialty udons will have beef, pork, or seafood.
Jigae - a thicker soybean soup base. Kimchi jigae (kimchee, tofu, pork) or dengjang jigae (beef, tofu, vegs) are the more popular ones.
Gook or tang - means soup. Mando guk is dumpling soup with beef and egg. Gom tang is oxtail soup with a white rich beef stock. Sullang tang is tender beef slivers in white rich broth. There are many many more soups, but these are my favorites.
Rice or noodles: Note "bap" means "rice".
Bibimbap - rice dish served in a very hot stone bowl. Most popular is dolsol bibimbap, which has veggies, bulgogi, a fried egg, and seasonings, served with sides of hot chili sauce and sesame oil. You get to mix everything together.
Bokumbap - Korean fried rice. Veggies, bulgogi, and rice topped with a thin egg omelette. Other variations are kimchi bokumbap (w/kimchi) or seafood bokumbap.
Japchae - This can be an entree or appetizer. Thin clear noodles with marinated beef and assorted seasoned veggies panfried.
There are many many things I'm leaving out, but these are dishes you'll find at any place, and they will be good, if you're at a good restaurant. With any entree, you'll get side dishes and perhaps some miso soup. The side dishes are called banchan, and include picked veggies of any kind, beans, egg, tofu, kimchee of any kind, or seaweed. The better the restaurant, the fresher and more banchan you get, in my opinion. Also, when you get a meat bbq, you usually get big leaves of lettuce, slices of garlic, korean chili peppers, hot chili sauce.
I'll add more pictures as I find them.