Body Piercing: Sources from Rabbi David Golinkin's Teshuva for the Masorti Va'ad Halakhah (Yoreh De'ah 182:5)
Questions from Reuven Resnick: May a girl or woman pierce her ear or nose and wear rings? May a boy or man pierce his ear or nose and wear rings? Is it permissible to pierce and wear rings on other parts of the body?

(מז) וָאֶשְׁאַ֣ל אֹתָ֗הּ וָאֹמַר֮ בַּת־מִ֣י אַתְּ֒ וַתֹּ֗אמֶר בַּת־בְּתוּאֵל֙ בֶּן־נָח֔וֹר אֲשֶׁ֥ר יָֽלְדָה־לּ֖וֹ מִלְכָּ֑ה וָאָשִׂ֤ם הַנֶּ֙זֶם֙ עַל־אַפָּ֔הּ וְהַצְּמִידִ֖ים עַל־יָדֶֽיהָ׃

(47) And I asked her, and said: Whose daughter art thou? And she said: The daughter of Bethuel, Nahor’s son, whom Milcah bore unto him. And I put the ring upon her nose, and the bracelets upon her hands.

(ד) וַיִּתְּנ֣וּ אֶֽל־יַעֲקֹ֗ב אֵ֣ת כָּל־אֱלֹהֵ֤י הַנֵּכָר֙ אֲשֶׁ֣ר בְּיָדָ֔ם וְאֶת־הַנְּזָמִ֖ים אֲשֶׁ֣ר בְּאָזְנֵיהֶ֑ם וַיִּטְמֹ֤ן אֹתָם֙ יַעֲקֹ֔ב תַּ֥חַת הָאֵלָ֖ה אֲשֶׁ֥ר עִם־שְׁכֶֽם׃
(4) And they gave unto Jacob all the foreign gods which were in their hand, and the rings which were in their ears; and Jacob hid them under the terebinth which was by Shechem.
(ב) וַיֹּ֤אמֶר אֲלֵהֶם֙ אַהֲרֹ֔ן פָּֽרְקוּ֙ נִזְמֵ֣י הַזָּהָ֔ב אֲשֶׁר֙ בְּאָזְנֵ֣י נְשֵׁיכֶ֔ם בְּנֵיכֶ֖ם וּבְנֹתֵיכֶ֑ם וְהָבִ֖יאוּ אֵלָֽי׃ (ג) וַיִּתְפָּֽרְקוּ֙ כָּל־הָעָ֔ם אֶת־נִזְמֵ֥י הַזָּהָ֖ב אֲשֶׁ֣ר בְּאָזְנֵיהֶ֑ם וַיָּבִ֖יאוּ אֶֽל־אַהֲרֹֽן׃
(2) And Aaron said unto them: ‘Break off the golden rings, which are in the ears of your wives, of your sons, and of your daughters, and bring them unto me.’ (3) And all the people broke off the golden rings which were in their ears, and brought them unto Aaron.
(יח) בַּיּ֨וֹם הַה֜וּא יָסִ֣יר אֲדֹנָ֗י אֵ֣ת תִּפְאֶ֧רֶת הָעֲכָסִ֛ים וְהַשְּׁבִיסִ֖ים וְהַשַּׂהֲרֹנִֽים׃ (יט) הַנְּטִיפ֥וֹת וְהַשֵּׁיר֖וֹת וְהָֽרְעָלֽוֹת׃ (כ) הַפְּאֵרִ֤ים וְהַצְּעָדוֹת֙ וְהַקִּשֻּׁרִ֔ים וּבָתֵּ֥י הַנֶּ֖פֶשׁ וְהַלְּחָשִֽׁים׃ (כא) הַטַּבָּע֖וֹת וְנִזְמֵ֥י הָאָֽף׃
(18) In that day the Lord will take away the bravery of their anklets, and the fillets, and the crescents; (19) the pendants, and the bracelets, and the veils; (20) the headtires, and the armlets, and the sashes, and the corselets, and the amulets; (21) the rings, and the nose-jewels;

(ו) יוצאין בסלע שעל הצינית, הבנות (קטנות) יוצאות בחוטין, ואפלו בקיסמין שבאזניהן. ערביות יוצאות רעולות, ומדיות פרופות, וכל אדם, אלא שדברו חכמים בהווה.

(6) A woman may go out with a Sela [a coin worth four Dinar] fastened on a corn [on her foot]; girls may go out with ribbons, and even with chips in their ears; Arabian women may go out in their veils, and Median women in their mantillas. So [indeed] may anyone, but the Sages speak of common custom.

(ח) קסדא - טמאה. ולחיים - טהורים. אם יש בהן בית קבול מים - טמאים. כל כלי המלחמה - טמאים. הכידון, הניקון, והמגפין, והשריון - טמאין. כל תכשיטי נשים - טמאים: עיר של זהב, קטליות, נזמים, וטבעות - וטבעת בין שיש לה חותם ובין שאין לה חותם - נזמי האף.

(8) A helmet is susceptible to impurity but the cheek-pieces are not susceptible. But if they have a receptacle for water they are susceptible to impurity. All weapons of war are susceptible to impurity: a javelin, a spear-head, metal boots, and a breastplate are susceptible to impurity. All women's ornaments are susceptible to impurity: a "city of gold" [a kind of tiara], a necklace, earrings, finger-rings, a ring whether it has a seal or does not have a seal, and nose-rings.

Men's Rings
(יא) וַיָּבֹ֣אוּ אֵ֠לָיו כָּל־אֶחָ֨יו וְכָל־אחיתיו [אַחְיוֹתָ֜יו] וְכָל־יֹדְעָ֣יו לְפָנִ֗ים וַיֹּאכְל֨וּ עִמּ֣וֹ לֶחֶם֮ בְּבֵיתוֹ֒ וַיָּנֻ֤דוּ לוֹ֙ וַיְנַחֲמ֣וּ אֹת֔וֹ עַ֚ל כָּל־הָ֣רָעָ֔ה אֲשֶׁר־הֵבִ֥יא יי עָלָ֑יו וַיִּתְּנוּ־ל֗וֹ אִ֚ישׁ קְשִׂיטָ֣ה אֶחָ֔ת וְאִ֕ישׁ נֶ֥זֶם זָהָ֖ב אֶחָֽד׃ (ס)

(11) Then came there unto him all his brethren, and all his sisters, and all they that had been of his acquaintance before, and did eat bread with him in his house; and they bemoaned him, and comforted him concerning all the evil that the LORD had brought upon him; every man also gave him a piece of money, and every man a ring of gold.

(כד) וַיֹּ֨אמֶר אֲלֵהֶ֜ם גִּדְע֗וֹן אֶשְׁאֲלָ֤ה מִכֶּם֙ שְׁאֵלָ֔ה וּתְנוּ־לִ֕י אִ֖ישׁ נֶ֣זֶם שְׁלָל֑וֹ כִּֽי־נִזְמֵ֤י זָהָב֙ לָהֶ֔ם כִּ֥י יִשְׁמְעֵאלִ֖ים הֵֽם׃ (כה) וַיֹּאמְר֖וּ נָת֣וֹן נִתֵּ֑ן וַֽיִּפְרְשׂוּ֙ אֶת־הַשִּׂמְלָ֔ה וַיַּשְׁלִ֣יכוּ שָׁ֔מָּה אִ֖ישׁ נֶ֥זֶם שְׁלָלֽוֹ׃ (כו) וַיְהִ֗י מִשְׁקַ֞ל נִזְמֵ֤י הַזָּהָב֙ אֲשֶׁ֣ר שָׁאָ֔ל אֶ֥לֶף וּשְׁבַע־מֵא֖וֹת זָהָ֑ב לְ֠בַד מִן־הַשַּׂהֲרֹנִ֨ים וְהַנְּטִפ֜וֹת וּבִגְדֵ֣י הָאַרְגָּמָ֗ן שֶׁעַל֙ מַלְכֵ֣י מִדְיָ֔ן וּלְבַד֙ מִן־הָ֣עֲנָק֔וֹת אֲשֶׁ֖ר בְּצַוְּארֵ֥י גְמַלֵּיהֶֽם׃

(24) And Gideon said unto them: ‘I would make a request of you, that ye would give me every man the ear-rings of his spoil.’—For they had golden ear-rings, because they were Ishmaelites. (25) And they answered: ‘We will willingly give them.’ And they spread a garment, and did cast therein every man the ear-rings of his spoil. (26) And the weight of the golden ear-rings that he requested was a thousand and seven hundred shekels of gold; beside the crescents, and the pendants, and the purple raiment that was on the kings of Midian, and beside the chains that were about their camels’necks.

This source seems to indicate that Israelite men did NOT wear rings, but rather it was an Ishmaelite custom.

דתניא: לא יצא החייט במחטו התחובה לו בבגדו, ולא נגר בקיסם שבאזנו, ולא סורק במשיחה שבאזנו, ולא גרדי באירא שבאזנו, ולא צבע בדוגמא שבצוארו, ולא שולחני בדינר שבאזנו,

A tailor must not go out with a needle stuck in his garment, nor a carpenter with a chip in his ear, nor a [wool] corder with the cord in his ear, nor a weaver with the cotton in his ear, nor a dyer with a [colour] sample round his neck, nor a money-changer with a denar in his ear; and if he does go forth, he is not liable, though it is forbidden: this is R. Meir's view.

However parallel sources read "nor a carpenter with a chip around his neck"
Does men wearing earrings or nose rings violate the prohibition against cross-dressing?
Sifre Devarim on Deuteronomy 22:5
"The garment of a man shall not be upon a woman" - the Torah uses the word abomination - a woman shall not dress the way a man dresses nor go out among the men,; this is basic idea: a man shall not be adorned in women's adornments nor go among the women. (This text is not generally accepted as normative halakhah)
Rambam Sefer Hamitzvot Lo Taseh 40:
"Any man who adorns or dresses in what is known in that place that it is a form specifically for women - is punished." (repeated in Tur (Yoreh De'ah 162) and Shulchan Aruch 162)
What if parents object?
(ג) אִ֣ישׁ אִמּ֤וֹ וְאָבִיו֙ תִּירָ֔אוּ וְאֶת־שַׁבְּתֹתַ֖י תִּשְׁמֹ֑רוּ אֲנִ֖י יי אֱלֹהֵיכֶֽם׃
(3) Ye shall fear every man his mother, and his father, and ye shall keep My sabbaths: I am the LORD your God.
איזהו מורא ואיזהו כיבוד מורא לא עומד במקומו ולא יושב במקומו ולא סותר את דבריו ולא מכריעו

What is "reverence" and what is "honor" [of one's parents]? "Reverence" is not to stand in his place, not to sit in his place, and not to contradict his words...

Rabbi Meir HaLevi Abulafia (1165-1244 Spain) These two expressions (in Kiddushin 31b) refer to halakhic arguments. But Rabbi Golinkin explains: "The plain meaning is that the phrase refers to all types of disagreement." (see Rabbi Hanananel 12th - 13th century, Pinchas Horovitz Frankfurt 1730-1805).
Rabbi Golinkin (20th - 21st Century Israel Masorti)
"Children and youth who want to pierce their bodies must consider not only their own desires but also the desires of their parents in order to keep the mitzvah of revering one's father and mother as it is explained according to the sources above."
Piercing of Sexual Organs - a precedent?
(נ) וַנַּקְרֵ֞ב אֶת־קָרְבַּ֣ן יי אִישׁ֩ אֲשֶׁ֨ר מָצָ֤א כְלִֽי־זָהָב֙ אֶצְעָדָ֣ה וְצָמִ֔יד טַבַּ֖עַת עָגִ֣יל וְכוּמָ֑ז לְכַפֵּ֥ר עַל־נַפְשֹׁתֵ֖ינוּ לִפְנֵ֥י יי

(50) And we have brought the LORD’S offering, what every man hath gotten, of jewels of gold, armlets, and bracelets, signet-rings, ear-rings, and girdles, to make atonement for our souls before the LORD.’

א"ר אלעזר עגיל זה דפוס של דדין כומז זה דפוס של בית הרחם. אמר רב יוסף: אי הכי, היינו דמתרגמינן מחוך ־ דבר המביא לידי גיחוך. אמר ליה רבה: מגופיה דקרא שמע מינה, כומז ־ כאן מקום זימה.

Rabbi Elazar (2nd-3rd generation Amora in Eretz Yisrael) said: "ear-rings" [better: "circular"] is a cast of female breasts; "girdles" is a cast of the womb. Said Rav Yosef, it that is the case, then we translate it mahok, [meaning] the place that leads to obscenity [gihuk]. Said Rabbah to him, It is implied in the very Writ itself: Kumaz=here [Ka-an] is the place [Mekom] of unchastity [Zimmah]....

Rashi in parallel sugya Berachot 34a comments on the word Kumaz - "cast of vagina that was done to their daughters and they would pierce the walls of the vagina as one pierces the ears and stuffs it so that they will not need men." This is as if to say that kumaz is a form of chastity belt.
Rabbi Golinkin: 4 reasons it cannot be a precedent for us: 1) what's referred to is a girdle, not piercing. 2) The purpose of what Rashi refers to is MODESTY as opposed to the widespread modern belief that piercing the sexual organs increases sexual pleasure. 3) Rabbah's explanation is a folk etymology. 4) modern scholars have a totally different explanation of the meaning of Kumaz and therefore the word sheds no light on the issue before us.
Keeping One's Body Healthy is a Mitzvah
Laws of Character Traits 4:1
Since maintaining a healthy and sound body is among the ways of God - for one cannot understand or have any knowledge of the Creator, if he is ill - therefore, he must avoid that which harms the body and accustom himself to that which is healthful and helps the body become stronger.

(ט) רַ֡ק הִשָּׁ֣מֶר לְךָ֩ וּשְׁמֹ֨ר נַפְשְׁךָ֜ מְאֹ֗ד...(טו) וְנִשְׁמַרְתֶּ֥ם מְאֹ֖ד לְנַפְשֹׁתֵיכֶ֑ם

(9) Only take heed to thyself, and keep thy soul diligently...(15) Take ye therefore good heed unto yourselves...

Hazal interpreted these phrases as a general warning to preserve one's health (see Berachot 32b)

(ד) ...וְכֵן כָּל מִכְשׁל שֶׁיֵּשׁ בּוֹ סַכָּנַת נְפָשׁוֹת מִצְוַת עֲשֵׂה לַהֲסִירוֹ וּלְהִשָּׁמֵר מִמֶּנּוּ וּלְהִזָּהֵר בַּדָּבָר יָפֶה יָפֶה. שֶׁנֶּאֱמַר (דברים ד-ט) "הִשָּׁמֶר לְךָ וּשְׁמֹר נַפְשְׁךָ". וְאִם לֹא הֵסִיר וְהֵנִיחַ הַמִּכְשׁוֹלוֹת הַמְּבִיאִין לִידֵי סַכָּנָה בִּטֵּל מִצְוַת עֲשֵׂה וְעָבַר בְּ(דברים כב-ח) "לֹא תָשִׂים דָּמִים":

Any stumbling block that endangers life, there is a positive mitzvah to remove it and to guard oneself against it and to be very very careful about it, as it says, "Only take heed to yourself and keep your soul diligently. If one did not remove it and left it for others to be endangered, one ignores a positive commandment and violates "do not bring bloodguilt" (Deuteronomy 22:8).

Conclusions
  1. It is clearly permitted for women and girls, men and boys to wear ear and nose rings.
  2. If parents object to body piercing, children and youth must seriously weigh the commandment of "revering one's father and mother" as explained above.
  3. Piercing sexual organs does not comport with Jewish values of tzniut (modesty) and should not be done.
  4. Medical risks exist with all types of body piercings. If someone decides to pierce his/her body, s/he is obligated to utilize all available precautions - as presented above - to fulfill the mitzvah of keeping oneself healthy.