Kosher fish are those that have both fins and scales. Common varieties include bass, flounder, pike, salmon, and trout.
All other seafood is not kosher. Examples of non-kosher seafood include fish like catfish and shark (no scales), as well as all shellfish, squid and eel (no fins or scales).
A good detailed list of kosher and non-kosher fish can be found on the kashrut.com.
