The Gemara (Berachot 51a) lists three rules that were taught by none other than the Angel of Death, one of which is that one cannot fulfill the Misva of the morning Netilat Yadayim by having somebody else pour water over his hands, unless that person had already washed his hands. As long as somebody's hands are still impure, he cannot bring purity to somebody else's hands. Only once a person has washed Netilat Yadayim in the morning can he then pour water on his fellow's hands for his fellow to fulfill the obligation. The Zohar comments that this is the hidden meaning of the verse (Bamidbar 19:19), "Ve'hiza Ha'tahor Al Ha'tameh" – "The pure shall sprinkle on the impure." This verse refers to the sprinkling of the Para Aduma waters, but it hints as well to the morning hand-washing, instructing that one whose hands are already pure may cleanse somebody else's hands.
In this respect, the morning Netilat Yadayim is treated more stringently than Netilat Yadayim before eating bread. Halacha allows a person to fulfill his obligation before eating bread by having someone else pour the water over his hands – even if that person did not first wash his hands, and even if that person has no intention of eating bread. For the morning Netilat Yadayim, however, only one who has already washed his hands can pour water over somebody's else's hands so he can fulfill his obligation.
This applies only to the actual pouring of the water. One may prepare a vessel of water for his fellow to use for Netilat Yadayim even before he has washed Netilat Yadayim.
The Bet Yosef brings different opinions among the Rishonim as to whether one may fulfill this obligation by having a gentile – such as a non-Jewish butler or personal attendant – pour water over his hands. In the Shulhan Aruch, Maran rules leniently. The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) recommended acting stringently in this regard, as did Rav Haim Palachi (Turkey, 1788-1868). (Interestingly, Rav Haim Palachi recommended acting stringently in this regard for the morning hand-washing, but felt that one may have a non-Jew pour water over his hands for Netilat Yadayim before eating bread.) Although Halacha follows the ruling of the Shulhan Aruch, and thus one may have a non-Jew pour water over his hands to fulfill the morning Netilat Yadayim requirement, it is proper to have specifically an observant Jew pour the water.
When a wife is a Nidda, Halacha forbids her from bathing her husband, or even washing just his hands, as this is an affectionate act that must be avoided during this time as a safeguard against marital relations. Therefore, a wife may not pour water over her husband's hands for the morning Netilat Yadayim when she is a Nidda. (Interestingly enough, the Hida writes that a woman who is a Nidda may not pour water over anybody's hands for the morning Netilat Yadayim, as her status of impurity precludes her from removing the impurity of somebody else's hands.)
The Rishonim debate the question of whether a wife who is a Nidda may prepare water for her husband to use for bathing. Rabbenu Yona (Spain, 1200-1263) ruled that this is forbidden, but other Rishonim ruled leniently, and Hacham Ovadia Yosef follows the lenient position. Hacham Ovadia adds that although several Ashkenazic Poskim maintained that a wife who is a Nidda should not prepare the bathtub for her husband, these Poskim would agree that she may fill a cup for him for the morning hand-washing, and bring him the cup, as this is done for the sake of a Misva. Several other recent Poskim concurred. Hacham Ovadia also allowed a wife who is a Nidda to turn on the faucet for her husband, adding that even those who rule stringently regarding the preparation for water would allow the wife to turn on the faucet when the husband is not present, or in his presence in an unusual manner.
The Kaf Ha'haim (Rav Yaakob Haim Sofer, Baghdad-Jerusalem, 1870-1939) writes that although it is obviously forbidden for a woman to bathe a man who is not her husband, she may, technically speaking, pour water over a man's hands. Preferably, however, this should be avoided. Hacham Ovadia questioned this ruling, as it seems that pouring water over another man's hands should be strictly forbidden. However, Hacham Ovadia allows a woman to prepare a utensil with water for another man.
Summary: One may fulfill the obligation of the morning Netilat Yadayim by having somebody else pour water over his hands, but only if that person had already washed Netilat Yadayim. One may fulfill the obligation with water that had been prepared by someone who had yet to wash his hands. One may have a non-Jew pour water over his hands to fulfill the morning Netilat Yadayim requirement. A woman who is a Nidda should not pour water over her husband's hands, but she may prepare the utensil of water for him. A woman should not pour water over another man's hands, but she may prepare the utensil of water for another man.