The Shulhan Aruch (Orah Haim 4:8) writes that one should perform Netilat Yadayim in the morning by washing his hands over a utensil, as opposed to washing them over the ground. The reason is that once the water comes in contact with the hands, it becomes impure, and if it then falls to the ground and people step on it, they can suffer harm as a result. Therefore, one should wash into a vessel, and then discard the water in a place where people will not come in contact with it. Of course, one fulfills his obligation regardless of where he performs Netilat Yadayim, but out of concern for the wellbeing of others, he should ensure that the water does not end up in a place where people walk.
Needless to say, the preferred place for washing Netilat Yadayim is in a sink, as the contaminated water descends right down the drain and into the sewer system, where nobody will tread on it. Nevertheless, this Halacha is relevant to those who sleep in a Sukka on Sukkot, and want to wash their hands in the Sukka or right outside the Sukka. They must wash into a utensil and then pour the water into a drain, safely away from people. Another situation where this becomes relevant nowadays is a camping trip. One must ensure when washing in the morning not to wash in a place where the water might be stepped on.
It is acceptable to wash on soft earth, such that the water is quickly absorbed into the ground, or on a hill such that the water right away descends to a place where nobody walks.
Some Poskim advise rinsing the sink after washing Netilat Yadayim, to clear it from the impurity of the water. If utensils used with food are in the sink, it is preferable not to wash Netilat Yadayim over the utensils, and to instead move them to the side. If one did wash over the utensils, he must ensure to wash them afterward, though, quite obviously, utensils in the sink are in any event dirty and waiting to be washed.
After one washes Netilat Yadayim, the water is forbidden for any type of benefit. It may not be used for watering plants, or given to a pet to drink.
Summary: The water used for Netilat Yadayim in the morning is considered impure, and could cause harm to those who step on it. Therefore, one who washes Netilat Yadayim outdoors must not do so in a place where people might step on the water. It is preferable after washing Netilat Yadayim in a sink to rinse the sink afterward. The water used for washing Netilat Yadayim is forbidden for any sort of benefit, and thus may not be used to water plants or given to pets to drink.