You cannot get paid for donating your body to science or donating your organs in the United States. The National Organ Transplant Act (Public Law 98-507), a federal law, makes it illegal to sell organs or tissues for profit. Violators are subject to prison time, a very hefty fine or both for engaging in organ sales. All states (there is variation from state-to-state on specifics) have passed some version of the Uniform Anatomical Gift Act, allowing individuals to donate as a gift their organs and tissues during their lifetime with the donation to take effect on their end of life.
Individuals donating organs and other parts are granted with a right for compensation which can be in a financial form or recognition. Different institutions also have varying policies on body donation.
In the US, you can't sell your body parts legally, but you can donate without getting paid. You will not get paid if you donate your body to science. The health insurance company usually should cover the costs when deciding to donate a live organ like a kidney. Your family also will not get paid.