Gemara

(Ravina): A Chacham came from Eretz Yisrael, and said that one who does not have water should clean his hands in earth, pebbles or chips of wood!

Support (Rava): It does not say "I will wash in water," rather, "b'Nikayon" -- in anything that cleanses!

Rav Chisda would curse one who delays praying until he can wash his hands with water.

Shabbos 109a (Beraisa - R. Noson): The Ru'ach that dwells on hands before washing is a Bas Chorin (dignified). It goes away only if each hand is washed three times, alternating.

Pesachim 111b: If one does any of the following without washing his hands (afterwards), he will be afraid, and he will not know why he is afraid:

Eating cress, letting blood, and cutting his hair or nails, he will be afraid for 30 days, seven days, three days, or one day, respectively.

Rishonim

Rosh (9:23): When one washes his hands in the morning, he blesses Al Netilas Yadayim. This is because a person's hands touch things, and it is impossible that he did not touch filthy flesh at night. They enacted a Berachah before he reads Keri'as Shema and prays. It would be appropriate to bless Al Nekiyus Yadayim, but since it was enacted to bless Al Netilas Yadayim for a meal, since one must wash from a Kli (which is called Natla), they enacted the same Berachah in the morning. If one has no water and cleans his hands with a pebble or earth, it seems that he blesses Al Nekiyus Yadayim, for one is obligated to clean his hands for prayer -- Erchatz b'Nikayon Kapai.

Question: Regarding matters that obligate Netilas Yadayim, is it enough to merely clean the hands without water?

Answer (Mordechai 193): One cannot bring a clear proof about this. We do not give (uncertain) answers for matters that involve danger. It is good to be stringent to wash with water.

Mordechai (195): One who does not have water should clean (rub) his hands in earth or pebbles, for it says "Erchatz b'Nikayon" -- in anything that cleanses. However, to eat bread, one must wash specifically with water.

Maharil (Teshuvah 23): Those who come from a cemetery to pray, it is good to wash the hands due to the Ru'ach ha'Tum'ah in a cemetery. Doresh El ha'Mesim is one who spends the night in a cemetery in order that Ru'ach ha'Tum'ah will dwell on him. Netilas Yadayim removes it. This is why we wash in the morning, for sleep is a 60th of death. R. Chananel and the Aruch explain that it is a Bas Melech, and goes away only if one washes three times (alternating). We wash again when returning to the Chatzer of the cemetery.

Poskim

Shulchan Aruch (OC 4:18): The following require Netilah with water: one who rises from the bed…

Beis Yosef (DH Kasav ha'Rav): The Avudraham brings from Tashbatz that seven things require washing with water - who rises from the bed, one who leaves the Beis ha'Kisei (privy) or bathhouse, cuts his nails, removes his shoes, touches his legs, or scratches his head. Also Kolbo says so. The Mordechai puts passing between the dead in place of rising from the bed. Mahari Avuhav brought these from Orchos Chayim, and adds one who touched a Mes or deloused his clothing. Some say that if one had marital relations and did not wash, his ways are messed up. Some say even one who touched a louse, or touched his body with his hand. Chazal say that if he did one of these and did not wash, if he is a Chacham, he will forget his learning. If he is not a Chacham, he will go crazy.

Taz (13): These require washing with water. It is not enough to clean the hands (with something else).

Magen Avraham (17): These require washing with water. One need not wash three times.

Kaf ha'Chayim (60): Machatzis ha'Shekel says that some of these matters are not due to Ru'ach Ra'ah, and do not require water, like the Magen Avraham himself (92:5) says. Tosefes Shabbos and Neve Shalom agree. However, Kisei Eliyahu and Yefe l'Lev say that all of them are due to Ru'ach Ra'ah. It seems that the Levush and Mishbetzos Zahav agree. One should be stringent to wash for all of them with water if it is available. Chayei Adam says so.

Mishnah Berurah (38): These are to remove the Ru'ach Ra'ah, therefore he should wash immediately, until the wrist, or in any case until the end of the fingers. If one soiled his hands with mud, which has no Ru'ach Ra'ah, he merely needs to clean the dirty place.

Kaf ha'Chayim (64): Whenever Netilah is required, even if only the pinky touched, he must wash until the wrist, or in any case until the end of the fingers.

Mishnah Berurah (39): For Tefilah, and all the more so for Torah, it suffices merely to clean the hands, like it says in Sa'if 22 about one who rose from a bed, and all the more so for the others. However, only water removes Ru'ach Ra'ah.

Shulchan Aruch (ibid.): … One who leaves the Beis ha'Kisei or bathhouse.

Magen Avraham (18): One who leaves a Beis ha'Kisei must wash immediately, just like (after waking) in the morning.

Shulchan Aruch (ibid.): … One who cuts his nails, removes his shoes, touches his legs, or scratches his head.

Mishnah Berurah (41): One who removes his shoes, touches his legs, or scratches his head need not wash due to Ru'ach Ra'ah. It is only due to cleanliness, therefore he need not wash immediately. The others are due to Ru'ach Ra'ah, so he must wash immediately.

Shulchan Aruch (ibid.): Some say, even one who passes between the dead.

Magen Avraham (20): This refers to a cemetery. Maharil says that one washes before praying near graves, and again when he returns to the Chatzer of the cemetery, for Shedim accompany him. One washes also the face.

Shulchan Aruch (ibid.): … One who had marital relations, or touched a louse, or touched his body with his hand.

Mishnah Berurah (45): Perhaps for a Pir'osh (flea), it suffices merely to clean the hands.

Shulchan Aruch (22): If one does not have water (after waking in the morning), he cleans his hands on a pebble, earth, or anything that cleans, and blesses Al Nekiyus Yadayim. This helps for Tefilah, but not to remove the Ru'ach Ra'ah.

Magen Avraham (24): One may clean in earth or on a board, whether his hands are dirty, or if he ceased guarding them.

Mishnah Berurah (55): If one has water, he must wash even for Minchah and Ma'ariv, even if he does not know about any filth. If he has no water, some say that he cleans with anything that cleans, lest something repulsive is stuck to his hands.

Mishnah Berurah (56): This helps even if his hands were Vadai dirty, e.g. he eliminated and cleaned himself.

Mishnah Berurah (57): He can clean with earth or a dry cloth. Since cleaning is in place of washing, he must clean the front and back until the wrist. B'Di'eved, if he cleaned until the end of the fingers, this suffices. It is not enough to clean just the fingertips.

Kaf ha'Chayim (100): If one is on a boat (and there are no pebbles or earth), he cleans on the wall of the boat or on stiff garments. The same applies on Shabbos, when he cannot use pebbles or earth, for they are Muktzeh.

Kaf ha'Chayim (101): Shirei Keneses ha'Gedolah brings from Birkas Avraham that one cleans three times. Olas Tamid and many others disagree, for it will not help for Ru'ach Ra'ah. The Beis Yosef brings from the Zohar that only water removes Ru'ach Ra'ah! Eliyahu Rabah answers that one answer in Birkas Avraham holds that also other things remove Ru'ach Ra'ah, and it is proper to be concerned for this opinion.

Kaf ha'Chayim (104): If one does not have enough water to wash three times, he washes once and blesses Al Netilas Yadayim, even though it does not help for Ru'ach Ra'ah. The Berachah is for sanctifying himself and removing Tum'ah, like a Kohen washes from the Kiyor. Since he pours only once, he must pour a Revi'is on both hands at once.

Shulchan Aruch (23): One may bless Birkos ha'Shachar before Netilas Yadayim, unless he slept naked. Then, he may not say Hash-m's name until he cleans his hands.

Beis Yosef (DH va'Yevarech): The Rosh connotes that one may bless Birkos ha'Shachar before Netilas Yadayim. He holds that the Berachah was enacted only for Keri'as Shema and Tefilah. The Rashba said that if one slept naked, since hands touch things, he may not say Hash-m's name until he cleans his hands with something.

Mishnah Berurah (61): The Pri Megadim says that even if he has water, for Berachos and Torah it suffices to clean his hands (with anything). The Gra connotes like this. The Zohar forbids blessing before washing. It is proper to be stringent if he has water.

Kaf ha'Chayim (107): The Zohar forbids any Berachah, or even one word of Torah, before washing. If one woke early and lacks water, he should wash a little or clean with anything, bless and learn, like the Gemara and Poskim say. Chalilah (Heaven forbid) ro be Batel from Torah!