If one, while getting ready to perform Netilat Yadayim, accidentally touches the water in the washing cup, is one still allowed to use that water for Netilat Yadayim, or does that person need to fill it up again with different water?
See here (from page 109) for a halachic discussion about this issue in a Chabad booklet. I'll only state here the final summarizing paragraph:
If one has touched the water deliberately (let's say, to clean one's hands) - the water is forbidden for both types of netilat yadayim (morning and before meals). However, if one has touched the water by mistake, it seems that for netilat yadayim in the morning, since one's hands were "impure" (teme'ot) - the water too became impure, and is forbidden for netilah. For netilat yadayim before meals, however, if touched by mistake - they are allowed. This is also true for water that is prepared for the morning netilah, which was touched during the night (if the person goes back to sleep).
The Rama (O"Ch 160:11) rules like the Terumas Hadeshen (#259) that touching the water before netilah does not invalidate the water for netilah. Similarly, the Mechaber (O"Ch 160:2) rules that one may take some water from a cup with his hand and use it for whatever purpose and then still use the left over water for netilas yadayim.