Gemara

13a (Mishnah): If a man does so (puts his hand to his Ever to check himself), his hand is worthy to be cut off!

(Beraisa #1 - R. Eliezer): One who holds his Ever while urinating causes a Mabul.

Chachamim: If he does not hold it, drops will fall on his feet, and people will think he is a Seris (who is impotent), and they will say that his children must be Mamzerim!

R. Eliezer: It is better that people say that his children are Mamzerim than for him to sin, even for a moment.

(Beraisa #2 - R. Eliezer (to Chachamim): He can stand in a high place, or in a place of loose earth, so drops will not fall on his feet, and he will not sin, even for a moment.

He gave Answer #2 first. Chachamim asked what to do if a high place or loose earth is not found. R. Eliezer said "it is better that people say..."

14a (Abaye): Kohanim who ride on camels may not eat Terumah. (This heats the Ever. Perhaps they had emissions.)

R. Yehoshua ben Levi cursed one who sleeps Perakdan (on his back; alternatively, face down).

One may sleep leaning slightly to the side.

43a (Mishnah): If a man was eating Terumah and felt his semen moving (it is about to come out), he should hold his Ever tightly (to delay the emission) until he swallows the Terumah.

Contradiction (Beraisa - R. Eliezer): One who holds his Ever while urinating causes a Mabul!

Answer #1 (Abaye): The Mishnah permits holding the Ever only through a thick cloth.

Answer #2 (Rava): He may use even a thin cloth. Once the semen starts moving, it will come out in any case.

Abaye forbids, lest this cause more semen to come out.

Rava holds that once the semen starts moving, holding the Ever will not cause more to come out.

Shabbos 118b (R. Yosi): I never looked at my Milah (Ever).

Question: Rebbi (Yehudah ha'Nasi) was called Rabbeinu ha'Kadosh because he never looked at his Milah. Also R. Yosi should have received this title!

Answer: Rebbi had another attribute. He never put his hands below his belt.

Nazir 59a (Rav Nachman): A Nazir may shave the underarms and genital area.

The Halachah does not follow Rav Nachman.

R. Ami sentenced a man to be lashed. His underarms were exposed, and R. Ami saw that he did not shave there.

R. Ami: Do not lash him. He is a Chacham.

(R. Chiya): One may not scratch there so that the hair will fall out.

Question (Rav): May one scratch through a garment?

Answer (R. Chiya): Yes.

Bava Basra 74a (Rabah bar bar Chanah): I saw those who died in the Midbar sleeping Perakdan. One had his knees bent. Our guide passed under.

Pesachim 108a: Perakdan is not considered reclining.

Zevachim 5a: Reish Lakish lied on his stomach and asked...

Rishonim

Rambam (Hilchos Isurei Bi'ah 21:19): A man may not intentionally cause Kishuy or to bring himself to lustful thoughts.

Rambam (23): A bachelor may not put his hand to Mevushav (the Beitzim, i.e. testicles), so he will not come to Hirhurim (thoughts that could lead to an emission). He should not even enter it below his navel, lest he come to Hirhurim. He may not hold the Ever while urinating. If he was married, it is permitted. In every case he should never put his hand to his Ever, except when he needs to eliminate.

Tosfos (Nidah 13a DH Im): Rebbi was called Rabbeinu ha'Kadosh because he never put his hand below his belt. The Chidush is that even though he was married, he was stringent.

Tosfos ha'Rosh (Gitin 47a): Reish Lakish used to lie on his stomach, like it says in Zevachim.

Tosfos (14a DH Afarkid): Bava Basra 74a supports that Afarkid means on the back. The Aruch says that it is face down.

Rashi (14a DH Afarkid): One may not sleep on his back, lest he have an erection and it will be noticeable to many. Alternatively, perhaps his hands will rest on the Ever and warm it.

Tosfos (14a DH Layit): The first Perush does not explain why it is forbidden when he is alone in the house! The Rashbam says that his garments will fall on the Ever and warm it. Some say that lying on the back warms the spine and causes erections, which can lead to emissions.

Tosfos (Pesachim 108a DH Perakdan): Our Gemara shows that Perakdan means on the back. People do not eat facing down!

Poskim

Shulchan Aruch (OC 3:15): Even a bachelor may help through the Beitzim.

Mishnah Berurah (29): This does not warm (the Ever). Sometimes one may hold the Ever while urinating, e.g. through a thick cloth, but not through his robe. Some question using a thick cloth, for we do not know the Shi'ur

Shulchan Aruch (16): A married man may hold the Ever only to urinate, but not to scratch it.

Beis Yosef (DH Kasuv): Semag says that the Ritz was unsure about this.

Magen Avraham (15): One may hold it through a thick cloth, for this does not warm it. See YD 182:3. This is unlike Divrei Chamudos (Nidah 2:2), who says that it is only for Terumah. If so, the Rif would not have brought it! (He brings only what is relevant nowadays.)

Gra: The Mishnah forbids a man to check. This connotes even a married man.

Mishnah Berurah (30): The Chayei Adam is stringent even through a thick cloth. One may comb the lower beard as long as he does not touch the Ever with his hand.

Bi'ur Halachah: Also a bachelor may touch below the crown only for urinating. I permit combing the lower beard, for this is no worse than touching through a thick cloth, especially according to Tosfos, who say that 'below the navel' means (only) the place of the Milah.

Kaf ha'Chayim (44): We can permit a married man to scratch below the crown through his robe, but a bachelor may not. The only Heter to hold it was for urinating, due to drops.

Kaf ha'Chayim (45): One may wash the area along with the rest of the body, but only if he does not look there, and he may not delay there.

Shulchan Aruch (OC 63:1): One may not recite Shma lying face down or on his back.

Gra (472:3): The Ran is concerned for both opinions of Perakdan. Perhaps both are called Perakdan. It is clear from Nidah that we are concerned lest this warm the Ever.

Aruch ha'Shulchan (5): The Gemara and Rashi connotes that face down is worse, lest the Ever be heated and this cause an emission.

Bi'ur Halachah (DH Aval): If he read Perakdan, b'Di'eved he was Yotzei.

Mishnah Berurah (6): One should accustom himself to lie on his side. It is a great Isur to lie face down or on his back.

Shulchan Aruch (EH 23:3): One may not intentionally cause Kishuy or to bring himself to lustful thoughts. Rather, if such thoughts come, he should divert his mind from folly to thoughts of Torah. Therefore, one may not sleep on his back with his face up. He must lean a little to the side, lest he come to Kishuy.

Gra (7): The Shulchan Aruch explains that the Isur of causing Kishuy is due to Zera l'Vatalah. The Ra'avad, and Tur and Shulchan Aruch (oc240:1) explain that it refers to (inciting his desire for) relations (with his wife above the proper times for intimacy).

Shulchan Aruch (4): One may not put his hand to Mevushav, lest he come to Hirhur. He should not even enter it below his navel for this reason. He may not hold the Ever while urinating. If he was married, it is permitted.

Beis Yosef (DH Kasav): The Zohar says that Zera l'Vatalah is the worst Aveirah in the Torah, therefore one must be very careful to avoid it.

Beis Shmuel (4): This connotes that a married man is permitted even if his wife is not with him.

Gra (11): 'Mevushav' refers to the Beitzim. The Rambam uses it to refer to everything around the Ever. This word is from the Torah. It is not precise, for even below the navel is forbidden! This is only for a bachelor. If not, what was so special about Rebbi?

Shulchan Aruch (YD 182:3): One may not scratch with his hand hair of the underarm or Ervah in order to make it fall out, but one may scratch with his garment to make it fall out.

Beis Yosef (DH Asur): This is the conclusion in Nazir 59a.

Bach (2): The Tur and Shulchan Aruch connote that one may scratch with his garment even in Beis ha'Ervah. Rashi connotes that the question was only regarding the underarm, but surely Beis ha'Ervah is forbidden even through a garment, due to Hirhur. R. Tarfon taught that a hand that goes below the navel should be cut off. This requires investigation.

Taz (3): Also Tosfos explains that the question was also about Beis ha'Ervah. Rashi said that it was only about the underarms. The Bach says that this is because surely Beis ha'Ervah is forbidden. There is no source in Rashi to say so. Also regarding shaving, Rashi explained the question regarding the underarms, even though surely it applies also to Beis ha'Ervah. Rashi mentioned only one of them. R. Tarfon cannot literally discuss the navel, for if so, what was special about Rabbeinu ha'Kadosh? Do not say that he was careful about below the navel, even though this is above the belt. Rather, R. Tarfon used a euphemism. This is why most people are not careful about this, only Rebbi was. The Rambam forbids putting one's hand to Mevushav, and says not to put it even below the navel. He taught these separately. He said 'forbidden' only regarding the first. The latter is only for extra Kedushah, lest he touch the Ever. Regarding the first he said 'so he will not come to Hirhur.' Regarding the latter he said 'lest he come to Hirhur.'

R. Akiva Eiger: See the Magen Avraham above (OC 3:14).

Shach (6): Rashi mentioned the underarms, and the same applies to Beis ha'Ervah. The Gemara in Nidah supports this. We permit through a thick cloth, for it does not warm!