Does dry pasta need washing? When I am cooking at home I usually cook with dry, store bought pasta shapes. Before I cook it I usually partly wash it under the tap so that the water isn't too cloudy when it cooks, I don't usually bother to wash it thoroughly so there is still some cloudiness. 

My question is basically, is it necessary to wash pasta before cooking it? Is there an advantage to washing it completely so it is boiling in clear water? I think it is just the starch that is being washed off (please correct me if I am wrong) so by washing it the cooked pasta would not stick together as much but I haven't tested it.
No, there's no need to wash the pasta, and really, it's best not to.

It's good that the water gets cloudy from the pasta starch. If it has enough starch in it, it'll leave the surface of the noodles a bit stickier, making sauce adhere better. And you can also use some of the pasta water in a sauce to the same end. Getting the water that starchy generally requires using less water (see What is the correct water to pasta ratio?). If you're using tons and tons of water, like the pasta package probably says, it's probably going to be too diluted.

The one case in which you might want to wash the pasta is if, even when you start it from cold water and stir enough, it sticks. The only kind of pasta I've had this happen with is orecchiette, which is shaped perfectly for getting it to stick to itself.