I was asked the question what is correct....
The crab trap.
or
The crab's trap.
which one is right??

The crab trap.

I know what you mean though. A trap for crabs as opposed to one which belongs to them. This is called the genitive case. Even if it were the genitive case though, it would be crabs' not crab's. Just to be clear though, the answer is crab trap.