Is larger cruise ship and merchant ship able to make right and left turn without tug boat to assist?

Modern cruise ships are highly maneuverable and rarely employ tugs. They have side thrusters. 

In the open sea, yes. In a channel or harbor probably not.

of course- thats why they have a steering wheel. They don't just point the ship at 89 degrees from NY harbor and hope to come near Spain.

Mostly yes, but it determines the equipment on the ship and the sharpness of the turn.
Most all ships have a rudder under the stern.  Some have bow thrusters.  Some have steerable propellers called "azipods".