The Shulhan Aruch (Yoreh De'a 116:1) writes that the Sages enacted a prohibition against drinking water that had been left exposed, due to the concern that a snake may have drunk some water and deposited venom in it. However, the Shulhan Aruch adds, in his time, snakes were not as common as they were in ancient times, and so this prohibition does not apply. The Tur (Rabbenu Yaakob Ben Asher, d. 1340) writes that when exposed water was forbidden for drinking, it was likewise unsuitable for Netilat Yadayim. Nowadays, however, when such water may be drunk, as there is no concern of snakes' venom, it may similarly be used for Netilat Yadayim. The Bayit Hadash (Rav Yoel Sirkis, Poland, 1561-1640) goes so far as to say that even those who refrain from drinking water that had been left exposed may use this water for Netilat Yadayim. However, in places where snakes are common, it is preferable not to use for Netilat Yadayim water that had been left uncovered. This is the ruling of Hacham David Yosef, in Halacha Berura.
Thus, if a person left water uncovered overnight, he may use that water for Netilat Yadayim in the morning, as snakes are not generally common in our neighborhoods. A Beracha may be recited over the washing.
If a person touched with his hand the water he wishes to use for Netilat Yadayim, the water has become contaminated, and is thus disqualified for Netilat Yadayim. If one has no other water with which to wash his hands, then he may use this water, but he should not recite a Beracha over the washing. The Eshel Abraham (Rav Avraham David Horowitz of Buchach, d. 1840) asserts that this Halacha applies only if one dipped his entire hand in the water. If only a finger touched the water, then it remains suitable for Netilat Yadayim.
If a person used the restroom and touched the water before washing, this does not disqualify the water for Netilat Yadayim.