There has been significant debate surrounding sturgeon, which has scales but is still not recognized as kosher by the major rabbinic bodies in the U.S. Why is this? Because only scales that can be easily removed from the fish without ripping the skin are recognized as scales for kosher purposes. Since sturgeon scales cannot be removed in this manner, the fish is not considered kosher.

Incidentally, since sturgeon is not considered kosher, neither is authentic caviar, the roe (eggs) of wild sturgeon.

For more, see All About Kosher Fish.