Almost all the fishes are edible, but not every species can be eaten raw. Under most conditions, fresh fishes are better but they may have parasites, so it is recommended to freeze before eating for safety issues. Sashimi has been popular in western countries for a long time and as a part of Japanese cuisine, sushi and fresh fishes have existed for centuries. Below are some fish species commonly used in sushi:
Salmon: Although salmon is widely welcomed and commonly used in fresh fish sushi, it's easily infected by parasites, so please freeze it before eating.
Clam, scallop and abalone: These mollusks are also popular in sushi, but try to avoid oysters. Oyster is not suitable for sushi rice though it's delicious.
Mackerel: Mackerel is called saba or aji in Japanese. All kinds of mackerels are good choices. As the frozen shime saba, it is treated with vinegar before being served.
Halibut or flatfish: Sushi menu may not have these English names. They are called "hirame" on the sushi menu. It is a good taste that making it as halibut slice.
Squid: Squid is common in sushi. Normally it's not eaten raw but quickly cooked before eating.