You can only use the Wii remotes with the Wii, but most games allow you to just use the buttons on the controller instead of the motion-sensor.
Yes, Nintendo has a "Wii Classic Controller" available for Nintendo Wii which closely resembles the controller of a Super Nintendo.
Also, some games (like the New Super Mario Brothers) let you turn the standard Wii remote sideways and use it like a normal Nintendo controller.