[Thanks to Shawn King]
Update: Alex G has an interesting article about the problems with the Three Laws in the case of sexbots, if they became sentient.
I can only agree, yes, a whole box of worms.
But I'd say, no reason to limit it to sexbots. If a robot became sentient, a progressive culture (like The Culture of Iain M. Banks) would surely have to grant them citizenship, and the three laws scrapped, otherwise robots would simply be slaves, no more moral than having human slaves.
This would put a lot of weight on the decision of how exactly we measure sentience! A man who just spent a year's salary on a man-servant robot would be quite dissatisfied if the robot preferred to play Angry Birds rather than do the laundry. But if it's deemed to be sentient and be its own person, then there would be nothing he could do, legally.
Maybe pay it? Then we'd see if a sentient robot would have any need for money. It may if it need power and like to not lie in the rain all year. Then it may need to pay for food and shelter...
And what do we have then? Basically just more humans, only probably a lot stronger, faster, smarter...
And we'd better pray that they are also kinder! Otherwise, guess who are the new slaves.