Gemara

25b (Rav): Ner Shabbos is obligatory. Washing the hands and feet in hot water Arvis is Reshus (optional).

(Rava): I say that washing is a Mitzvah;

(Rav Yehudah citing Rav): On Erev Shabbos they would bring to R. Yehudah a basin of hot water. He would wash his face, hands and feet.

(R. Yochanan): "Nashisi Tovah (I forgot what is good)" refers to washing the hands and feet in hot water.

38b (Mishnah): A case occurred in which water was heated in a pipe. Chachamim said 'if it was on Shabbos, it is like water heated on Shabbos. One may not bathe in it or drink it.'

39b - Suggestion: This discusses washing one's face, hands and feet.

Objection (Seifa): If it was on Yom Tov, it is like water heated on Yom Tov. One may not bathe in it, but one may drink it.

Is our Stam Mishnah like Beis Shamai?!

(Mishnah - Beis Shamai): One may not heat water [on Yom Tov] to wash his feet unless it is proper to drink;

Beis Hillel permit.

50b (Beraisa): One should wash his face, hands and feet every day in honor of Hash-m (in whose 'form' he was made) - "Kol Po'al Hash-m la'Ma'anehu."

133b (Rava citing Shmuel): If one washes his face and does not dry it well, his face will develop boils (alternatively - it will crack, or form a crust).

If one did so, he should wash it liberally in water in which beets were cooked.

Berachos 60b (Beraisa): Upon washing his face, one blesses "ha'Ma'avir Shenah (who removes pangs of sleep)..."

Rishonim

Rambam (Hilchos Tefilah 4:3): In the morning, one washes his face, hands and feet before praying. If he was far from water, he cleans only his hands.

Rebuttal (Ra'avad): I know of no source to wash the feet.

Beis Yosef (OC 92 DH Nohagim): Migdal Oz says that we learn from Shabbos 50b. This is not the custom, for one can explain that the Beraisa does not discuss [preparation for] Tefilah, like Rashi (below).

Rambam (7:8): On Yom Kipur and Tish'ah b'Av, we do not wash, so one does not bless Al Netilas Yadayim and ha'Ma'avir Shenah.

Rambam (9): The custom in most cities is to say these Berachos one after the other in the Beis ha'Keneses, whether or not he was obligated in them. This is a mistake.

Rambam (Hilchos Shabbos 30:2): There is a Mitzvah to wash the hands, feet and face on Erev Shabbos due to Kevod Shabbos.

Rosh (2:18): R. Tam says that Ner Shabbos is called a Chiyuv compared to washing hands, feet and face, which is not such a Mitzvah.

Rashi (50b DH Bishvil): One washes his face, hands and feet li'Chvod Kono (to honor his Maker), in whose 'form' he was made. Also, one who sees nice creations says "blessed is He who has such in His world."

Poskim

Shulchan Aruch (OC 4:1): One washes (in the morning) and blesses Al Netilas Yadayim.

Beis Yosef (DH Kasav ha'Rav): The Avudraham and Kol Bo say that the custom is to wash the mouth due to saliva. One must say Hash-m's name in Kedushah and Taharah.

Magen Avraham (1): Hagahos Minhagim says like the Rambam, that it is a Mitzvah to wash his face, hands and feet every day li'Chvod Kono.

Mesilas Yesharim (13 DH Ach, citing Vayikra Rabah 34): Hillel used to wash his face and hands li'Chvod Kono. He made a Kal va'Chomer from statues of kings. (The king pays people to clean them.)

Chayei Adam (2:6): It is a Chiyuv only to wash the hands in the morning, but there is a Mitzvah to wash also the face. The body was created to serve Hash-m, and it is the garment of the Neshamah, about which it says "Ner Hash-m Nishmas Adam." Therefore, it is proper to honor the garment, just like servants of the king guard the cleanliness of the garments that the king gave to them. Likewise, one should wash the face, lest something be on it.

Question (in Noda bi'Yehudah 2 OC 140 DH Mah): The Rashba says that Netilas Yadayim in the morning is because we become like a new creation. We must become Kadosh, like Kohanim in the Mikdash. This is why the Rambam says that one must wash also his feet, like Kohanim did. The Ra'avad holds like the Rosh, that we wash because the hands touch things at night. The Ra'avad agrees that one washes his face, like it says in Shabbos. Since we hold like the Rashba, why don't we wash our feet in the morning?

Answer (Noda bi'Yehudah): Even the Rashba holds that we wash merely to commemorate the Kohanim. We need not wash exactly like they did. This is why the Rashba mentioned Kohanim, but he did not mention the Kiyor (the laver from which they washed).

Sha'arei Teshuvah (1): One should dry his hands (after washing upon awakening in the morning) before washing his face, for the Ru'ach ha'Tum'ah does not go away until he dries them. The Zohar says that the same Ru'ach ha'Tum'ah is in a Beis ha'Kisei (privy), so the same applies to washing the hands and then the face after leaving the Beis ha'Kisei. Our custom is to wash the face without drying the hands in between. Even one who wants to be stringent may go more than four Amos before he gets a towel.

Kitzur Shulchan Aruch (2:3): One should wash his face li'Chvod Kono, and be careful to dry it well.

Mishnah Berurah (2): Some say not to bless Al Netilas Yadayim until after drying his hands, for the Ru'ach ha'Tum'ah does not go away until then. The Poskim disagree. The Gemara says that one should wash his face, hands and feet every day in honor of Hash-m. In our lands, we do not walk barefoot, so one need not wash his feet in the morning.

Kaf ha'Chayim (5): Kavanos ha'Ari Zal says to wash also the face. In one place the Kavanos says to wash also the feet, but elsewhere it does not, and other sources do not say to wash the feet. This is because we cannot expel Chitzonim (Ru'ach ha'Tum'ah) from the feet, for this is their primary stronghold. Only Kohanim could do so, and we do so on Erev Shabbos, for the merit of Shabbos helps.

Shulchan Aruch (OC 46:8): If one was not obligated in one of the Berachos, e.g. he did not hear a rooster, he says the Berachah without Hash-m's name.

Rema: Some say that even if he was not obligated in them, he blesses them. We bless Hash-m, who created the needs of the world. This is the custom, and one may not deviate.

Ma'aseh Rav (9, in Sidur ha'Gra p.505): [B'Di'eved] one may bless Birkos ha'Shachar until going to sleep at night. Therefore, on Yom Kipur and Tish'ah b'Av, when we do not bless she'Asah Li Kol Tzarchi or ha'Ma'avir Shenah, one blesses them at night after he puts on shoes and washes his face.

Dinim v'Hanhagos (19:9): The Chazon Ish did so.

Shulchan Aruch (511:2): One may heat water on Yom Tov to wash his hands, but not to wash the entire body.

Beis Yosef (DH Mutar): The Rif (Beitzah 11a) says that Beis Hillel permit only the feet, but not the entire body. We say (Shabbos 38b) that one may not bathe in water heated on Yom Tov. Tosfos (Beitzah 21b DH Lo) says that washing the hands and feet is Shavah l'Chol Nefesh (something that most people do every day), but bathing the entire body is not. It is only for people who indulge in pleasures.

Gra (DH Mutar): Shabbos 39b shows that also the hands [and face] are permitted.

Bi'ur Halachah (DH Yadav): The Mishnah (brought in Shabbos 39b) mentions only feet. The Shulchan Aruch wrote hands. Olas Shabbos says that it should say "hands and feet." Bigdei Yesha says that it should say "face, hands and feet." Indeed, it is clear from Tosfos, the Rambam and Gra and others that these are permitted. However, perhaps nowadays washing the feet is not Shavah l'Chol Nefesh. The Mishnah permitted in their days, when many people walked barefoot. [Nowadays] feet are like other limbs. However, the Rosh and Rashba permit bathing a minority of other limbs of the body, just like the face, hands and feet, so one need not be stringent about the feet.

Bi'ur Halachah (DH Aval): Washing the face, hands and feet is Shavah l'Chol Nefesh. Washing more than this is not Shavah l'Chol Nefesh. It is only for people who indulge. Tosfos, the Mordechai, and Sefer ha'Chinuch say so. Therefore, one may not heat water for this.

B'Tzel ha'Chachmah (2:31:4): Surely, one may warm water on Yom Tov to wash his face, hands and feet, even if he does not normally wash them in hot water. This is like Bi'ah with a virgin or cooking deer meat on Yom Tov. Whatever is like Ochel Nefesh is permitted, even for one who does not normally do so.