Our middle son went through a phase of being obsessed with winning stuffed animals from claw machines. I said that we could build one in the basement.
Rather than building a sturdy box, the claw machine hangs from the exposed joists in the basement. To the joists are attached two IKEA Vidga curtain tracks. From these hangs a board that supports the third curtain track running the other way. Because I was out of lego motors, I used Kinex motors winding along shoelaces to move the claw mechanism down the tracks. From this Kinex structure hangs the LEGO system, with a winch and claw. The claw is designed to actually pick up items with a reasonably strong grip.... not as frustrating as the ones in the store that take your money. One arm extending out from the claw guides the claw motor wire to avoid tangles, the other side has a counterweight of pennies.
This system was controlled using an Arduino, since my RCX is dead.
For a controller, I salvaged a joystick from a toy robot.
In action: