Related to Are there any jokes in the torah?, what puns exist in Tanach?
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The Ibn Ezra, in his commentary to Bereishis 2:25, gives the following examples:
One means "naked," and one means "cunning."
One means "donkey," and one means "many heaps."
One means "donkeys" and one means "cities."
He also asserts in his commentary to Shemos 22:5 that this is another example of a pun:
In the first verse, they all are related to the word "animal," while in the second it refers to fire.
This article, by Professor Gary Rendsburg of Cornell University, provides a number of examples of puns (some of them bilingual) from throughout Tanakh. As you can see from the final page, it is an article within a collection that deals explicitly with this issue.
My personal favourite from the ones that he cites, and he cites many, is a Hebrew/Greek bilingual pun in Proverbs 31:27. Rather than say צופה הליכות ביתה ("she watches over the ways of her household"), a more unusual form of the verb, צופיה, is used, and one which allows the author to pun on the Greek word for wisdom (sofia).
Most importantly, the article is replete with references to other texts (many of them by the same author, though not all of them), which explore other more specific examples of biblical Hebrew wordplay.
Moshe rabbeinu made a couple, according to Rashi:
Shmos 32:18 וַיֹּאמֶר, אֵין קוֹל עֲנוֹת גְּבוּרָה, וְאֵין קוֹל, עֲנוֹת חֲלוּשָׁה; קוֹל עַנּוֹת, אָנֹכִי שֹׁמֵעַ.
(The dagesh on עַנּוֹת drives the point home.)
Bamidbar 21:9 וַיַּעַשׂ מֹשֶׁה נְחַשׁ נְחֹשֶׁת Which, according to Rashi, was a bit of a pun.
Yeshaya 5:7 וַיְקַו לְמִשְׁפָּט וְהִנֵּה מִשְׂפָּח, לִצְדָקָה וְהִנֵּה צְעָקָה. Rashi explains מִשְׁפָּט/מִשְׂפָּח and צְדָקָה/צְעָקָה are used because they sound similar.
I've always been enamored with Bamidbar 19:17: וְנָתַן עָלָיו מַיִם חַיִּים, אֶל-כֶּלִי. I'm waiting to be at a meal with a person name Kelly, who asks someone (not next to her) to pass the Mayim Chaim (brand of soda pop). When the person passes it over the man sitting next to Kelly, he will place it on his head, reciting this verse.
I also like Bamidbar 22:30 הֲלוֹא אָנֹכִי אֲתֹנְךָ אֲשֶׁר-רָכַבְתָּ עָלַי מֵעוֹדְךָ עַד-הַיּוֹם הַזֶּה
I hear it as "Hello?! Am i not your donkey?! ..." This works for any הֲלוֹא, but i like that one best.
Here are two of my favorite:
Bamidbar 24:10–11: והנה ברכת ברך זה שלש פעמים׃ ועתה ברח־לך אל־מקומך; you have continually blessed (barekh) them three times. Now flee (b’raḥ) to your place.
Devarim 11:16–17: ועבדתם אלהים אחרים … ואבדתם מהרה; lest you serve (va‘avadtem) strange gods … you will quickly be banished (va’avadtem).
What of Bereishit 29:10 and 11?
The verbs here are very similar (only the vowels change). This makes it both a pun and a trap for bad baalei kriah.
I'm wondering if אברהם gave 7 sheep to אבימלך as witness that the wells belong to אברהם (Breishis 21:30), and then אברהם and אבימלך swore their treaty, and באר שבע is named because of the swearing (שבועה). I wonder if אברהם picked 7 animals because the word שבע with a סגול sounds like שבע with a פתח, and it's just a play on words.
Also ובן משק ביתי הוא דמשק אליעזר (Breishis 15:2). Depending on how you translate the words בן משק and דמשק, if they aren't related on a pshat level, but are put together because they sound similar, that may be a play on words.
Edit: I thought of another possibility. יצחק is named so because of the laughing of אברהם and שרה, which are different but share the meaning "laughing". Then שרה says "שחוק עשה לי", a different type of laughter. Then ישעמאל is מצחק - something that is also a very different type of laughter.
Ex 13:14 ויהי בשלח פרעה את העם ולא נחם אלהים דרך ארץ פלשתים כי קרוב הוא כי אמר אלהים פן ינחם העם בראתם מלחמה ושבו מצרימה