The stand of Hinduism is very clear when it comes to Organ Donation. Since organ donation is a good deed and aims at saving someone's life, there is no religious law which prohibits this practise. It is considered as one of the finest things a human being can do; good karma to put it in the Hindu way. The Hindu scriptures refer to this good deed as "Daan" which also means selfless giving.
Organ donation is one of the purest forms of daan that a Hindu or for that matter, any individual can perform. What can be better than saving a human life?