How much he loved Mitzvot: Succah 41b
Became sick after marrying a Kohenet, and said that the Kehunah had rejected him: Pesachim 49a
Arguing a position, based on "I heard it [this law] stated explicitly!": Niddah 8b
R' Yehoshua responded jokingly to an orphan who pressed him, jokingly, with practical questions about honoring one's parents: Kiddushin 31a
Was put into a suspicious position when he had to argue for the Jews with a Roman patron, but onlookers knew to judge him favorably: Shabbat 127b
Publically bathed on a fast day which had been decreed on Chanukah: Rosh HaShanah 18b
Testifying with R' Papyas regarding a law: Temurah 18a
Anecdotes Involving R' Eliezer
Called "Yehoshua" by R' Eliezer in a debate: Pesachim 65b; Kiddushin 32b
Rabban Gamliel tried to serve R' Eliezer, R' Yehoshua and R' Tzaddok at Rabban Gamliel's son's wedding. R' Eliezer refused to be served, but R' Yehoshua and R' Tzaddok pointed to Avraham's and Gd's service of others, respectively, as models for the greater serving the lesser: Kiddushin 32b Onkelostranslated the Torah into Aramaic, transcribing from the words of R' Eliezer and R' Yehoshua: Megillah 3a
R' Eliezer said to R' Yehoshua, "You haven't heard as much as I have, so you can't declare what the law is!": Niddah 7b
A certain law was practiced like R' Yehoshua while R' Eliezer was alive, as R' Yehoshua wanted to keep people from errantly following R' Eliezer for other things, but after his death R' Yehoshua returned the practice to that advocated by R' Eliezer: Niddah 7b
Conflict with R' Eliezer as to when to flip over the beds in mourning for Rabban Gamliel: Moed Katan 27a
R' Eliezer and R' Yehoshua, students of R' Yochanan ben Zakkai, carrying him out of Jerusalem to the Roman general Vespasian: Gittin 56a
Anecdotes involving other Sages
Rabban Gamliel vs. R' Yehoshua regarding the calendar, and R' Yehoshua giving in: Rosh HaShanah 24b-25a, 25b
R' Akiva and R' Dosa ben Harkinas comforting R' Yehoshua, when Rabban Gamliel forced him to forego his own ruling for Rabban Gamliel's: Rosh HaShanah 25a, 25b
Rabban Gamliel, R' Yehoshua, R' Elazar ben Azaryah and R' Akiva on a boat: Succah 41b
Rabban Gamliel tried to serve R' Eliezer, R' Yehoshua and R' Tzaddok at Rabban Gamliel's son's wedding. R' Eliezer refused to be served, but R' Yehoshua and R' Tzaddok pointed to Avraham's and Gd's service of others, respectively, as models for the greater serving the lesser: Kiddushin 32b
R' Akiva, R' Yehoshua, Rabban Gamliel and R' Elazar ben Azaryah were at sea on Shabbat. R' Akiva and R' Yehoshua chose to be strict on themselves and remain in a four-cubit space, whereas Rabban Gamliel and R' Elazar ben Azaryah travelled the breadth of the boat: Eruvin 41b
R' Akiva, R' Yehoshua, Rabban Gamliel and R' Elazar ben Azaryah were at sea on Shabbat, and arrived at a port on Shabbat. The sages asked Rabban Gamliel what they could do, and he replied they were all right, since he had noted their arrival within the borders of the town before Shabbat began: Eruvin 41b, 43a
Rabban Gamliel, R' Elazar ben Azaryah and R' Yehoshua cried about the happiness of Roman idolaters as compared to the destruction of the Temple, but R' Akiva laughed, saying that those who follow Gd will be all the more rewarded, as compared to those idolaters: Makkot 24a-b
Rabban Gamliel, R' Elazar ben Azaryah and R' Yehoshua cried when they saw a fox walking in the former Holy of Holies, but R' Akiva laughed, saying that just as the prophecy of a fox walking there had been fulfilled, so the prophecy of the Jewish elders returning to the streets of Jerusalem would be fulfilled, too. The sages responded, "Akiva, you have comforted us, Akiva, you have comforted us!": Makkot 24b R' Akiva asking questions of Rabban Gamliel and R' Yehoshua in a butcher's shop in Imaum: Makkot 14a; Keritot 15a-b Rabban Gamliel and Rabbi Yehoshua going to purchase an animal for Rabban Gamliel's son's wedding feast: Makkot 14a; Keritot 15a
R' Yehoshua labelling Rabban Gamliel, "Berebi [Leader of the Generation]": Kiddushin 32b Onkelostranslated the Torah into Aramaic, transcribing from the words of R' Eliezer and R' Yehoshua: Megillah 3a
R' Yehoshua once ruled according to stringent view of the school of Shammai, and when his students complained that he was extending a period of discomfort for them, he responded that he was extending their share in the World to Come: Niddah 16b
After Rabban Gamliel died, R' Yehoshua tried to change a certain legal practice. R' Yochanan ben Nuri arose and said, "It appears to me that the body should follow the head [those who came first]! We always followed Rabban Gamliel in his days, now you want to annul his words? Yehoshuam we will not listen to you, for the law is established like Rabban Gamliel!" No one argued against him.: Eruvin 41a
R' Akiva called "Akiva" by R' Yehoshua: Rosh HaShanah 25a; Makkot 24b
R' Akiva calling R' Yehoshua "Rebbe": Rosh HaShanah 25a
R' Akiva reporting the practice of Rabban Gamliel and R' Yehoshua, presumably to consider that as the correct practice: Succah 37b
Was Called "Bar Livai [Son of Levi]" by R' Chanina: Shabbat 156a
Upset with R' Elazar Chisma and R' Yochanan Ben Beroka for not wanting to tell him R' Elazar Ben Azaryah's statements from the Study Hall: Chagigah 3a
R' Yehoshua Saying that a generation isn't orphaned if R' Elazar Ben Azaryah lives in it: Chagigah 3b
R' Yehoshua was expert in the laws of grafted produce; nonetheless, he went to R' Yochanan ben Nuri to ask him a question regarding those laws: Eruvin 11b
Rabbi Yehoshua standing against Rabbi Eliezer despite Divine support for Rabbi Eliezer: Bava Metzia 59b Rabbi Akiva replying to Rabbi Yehoshua: If your halachic statement is a received tradition, I accept it. If it is a result of "kal vachomer" logical deduction, though, then I can refute it thus: Keritot 15b