I've always noticed people that make sure their hands are perfectly dry before washing (i.e. washing for eating bread). Why do people do so? Where does this apparent stringency come from?
According to the Chazon Ish (Orach Chaim 24:20) they must be completely dry before washing or the washing is invalid b'dieved. According to the Mishna Berura (Beiur Halachah 162:2) they may even be completely wet before washing. The Baal haTanya apparently holds in his Shulchan Aruch like the Mishna Berura but rules in his siddur like the Chazon Ish.
I know that I have a minhag from my grandparents in Russia, that they would wash and dry their hands before ritual washing. The reason is, that if one's hands were dirty, it would create a chatzitzah (barrier) between one's skin and the water being poured. That is why they would wash their hands. As for drying them before washing netilas yadayim, perhaps they did that to prevent any (safek) tamei water that is already on one's hands from making the water of netilas yadayim tamei as well. The same would seem to apply here regarding just drying one's hands.