Strict vegetarians will have a tough time in Korea unless they're willing to stick to side dishes. About the only Korean vegetarians around are the most pious Buddhist monks. The whole concept is generally a mystery to everyone else. There are a few dishes that can be ordered without meat, but a vegetarian wanting to really sample a variety of Korean food would have to try one of the few Buddhist vegetarian restaurants in Seoul.
Those who eat seafood will have no problem, however, since being on a peninsula has made fish a common element in the diet. You can find seafood on any street or back alley, especially where people are drinking.
After the Japanese were finally forced out, udon noodle soups and raw fish were the culinary survivors. Udon, pronounced 'udong' here, is a popular lunch dish, while sushi and sashimi (known as hwae here) are the most expensive dinner options around. There has also been an interesting metamorphosis of rolled sushi--into a fishless rice and seaweed roll known as 'kimbap.' This ubiquitous snack food generally features ham, several vegetables or kimchi, pickled radish, and a bit of egg. Sometimes you can find a version with just kimchi and no ham.