Can Muslims eat fish? Is fish halal?

Short answer: yes! Muslims can eat practically all types of fish, including those without scales or fins (e.g. whales and eels, respectively), and can be eaten raw/cooked/fried.

Long answer: All fish are considered halal. Fish do not require to be ritually slaughtered like cows, chickens, and other land animals. Thus, whoever or however the fish is prepared or killed doesn't require scrutiny, though naturally, Muslims will keep to proper methods. Keep in mind that adding something like alcohol to the meal, as they do in some sushi places, does render the fish haram or impermissible to eat. 

There are groups of Muslims, like Hanafis from the Indian subcontinent, who do not eat sea creatures like oysters, crab, lobsters, octopus, and shrimp. They are not considered to be "fish" or "fish-like" and therefore disliked (makhruh). Other Muslims, like Shafis from Egypt, will eat them as they deem "anything under the sea" to be fish/halal. Both are acceptable when properly followed.