The Zohar, in Parashat Vaysheb (cited in Bet Yosef, Orah Haim 4), writes that when one washes Netilat Yadayim in the morning, he must wash his hands over a Keli (utensil). Meaning, not only must the water be poured from a utensil, but the pouring must be done over a utensil. The common practice nowadays, of course, is to wash Netilat Yadayim over a sink. As a sink is not a Halachic "Keli," the question arises as to whether this practice is acceptable, or if perhaps we should be doing Netilat Yadayim differently.
Maran, in codifying this Halacha (Orah Haim 4), writes, "One should not wash over the ground, but rather into a utensil." The first clause in this sentence – "One should not wash over the ground" – implies that the Zohar’s intent is not that one must wash into a utensil, but rather that one must not wash over the ground, as people may then step onto the waters. In the second clause, however, Maran explicitly writes that the washing must be done into a utensil. Thus, we have contradictory implications in the Shulhan Aruch, and the question now becomes which implication is the Halachically authoritative one.
Hacham Abraham Antebbi (Aleppo, 1765-1858), in his Mor Ve’ohalot (Hoshen Mishpat 21), establishes the rule that when we find a passage in the Shulhan Aruch with contradictory implications, we should follow the implication of the earlier clause. And so in our case, with regard to the morning Netilat Yadayim, we follow the implication of the phrase, "One should not wash over the ground." Accordingly, the requirement is to ensure that the water does not fall to the ground, and not that it falls specifically into a Halachic "Keli." Indeed, Hacham Ovadia Yosef rules in his Yabia Omer (vol. 5, Orah Haim 2) that one may wash in any manner which does not allow the water to fall to the ground. This is also the position of the Kabbalist Hacham Yaakov Hillel (contemporary), in his work Vayashab Ha’yam (vol. 1, Orah Haim 2), based on the writings of Hacham Shaul Ha’kohen Dweck (the "Sadeh," 1857-1933). Therefore, it is certainly permissible to wash Netilat Yadayim over a sink, and, in fact, it is preferable to do so. If one washes over a utensil, he must then discard the water, which in the interim may spill to the ground. By washing directly over a sink, one ensures that the water will be immediately discarded, as it goes straight into the drain and into the sewer system.
It should be noted that if there are dishes in the sink, it is permissible to wash Netilat Yadayim over the dishes, as long as the dishes are washed before they are used with food. The water does not create a permanent state of Tum’a (impurity), and thus the dishes may be used after they are rinsed. Of course, dishes in the sink are usually there because they need to be washed, so it is certainly acceptable to wash over dirty dishes in the sink.
(These Halachot appear in Mehkereh Eretz, vol. 3 Orah Haim 2.)
Summary: When washing the morning Netilat Yadayim, one must ensure that the water used for washing does not fall to the ground, and thus the most preferred method is to wash directly over a sink. One may wash over a sink with dishes in it, as long as the dishes are then rinsed before they are used for food.