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
Rabbi 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 Rabbi Papyas regarding a law: Temurah 18a
Anecdotes Involving Rabbi Eliezer
Called "Yehoshua" by Rabbi Eliezer in a debate: Pesachim 65b; Kiddushin 32b
Rabban Gamliel tried to serve Rabbi Eliezer, Rabbi Yehoshua and Rabbi Tzaddok at Rabban Gamliel's son's wedding. Rabbi Eliezer refused to be served, but Rabbi Yehoshua and Rabbi Tzaddok pointed to Avraham's and Gd's service of others, respectively, as models for the greater serving the lesser: Kiddushin 32b
Rabbi Eliezer said to Rabbi 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 Rabbi Yehoshua while Rabbi Eliezer was alive, as Rabbi Yehoshua wanted to keep people from errantly following Rabbi Eliezer for other things, but after his death Rabbi Yehoshua returned the practice to that advocated by Rabbi Eliezer: Niddah 7b
Rabbi Eliezer and Rabbi Yehoshua, students of Rabbi Yochanan ben Zakkai, carrying him out of Jerusalem to the Roman general Vespasian: Gittin 56a
Anecdotes involving other Sages
Rabban Gamliel vs. Rabbi Yehoshua regarding the calendar, and Rabbi Yehoshua giving in: Rosh HaShanah 24b-25a, 25b
Rabbi Akiva and Rabbi Dosa ben Harkinas comforting Rabbi Yehoshua, when Rabban Gamliel forced him to forego his own ruling for Rabban Gamliel's: Rosh HaShanah 25a, 25b
Rabban Gamliel, Rabbi Yehoshua, Rabbi Elazar ben Azaryah and Rabbi Akiva on a boat: Succah 41b
Rabban Gamliel tried to serve Rabbi Eliezer, Rabbi Yehoshua and Rabbi Tzaddok at Rabban Gamliel's son's wedding. Rabbi Eliezer refused to be served, but Rabbi Yehoshua and Rabbi Tzaddok pointed to Avraham's and Gd's service of others, respectively, as models for the greater serving the lesser: Kiddushin 32b
Rabbi Akiva, Rabbi Yehoshua, Rabban Gamliel and Rabbi Elazar ben Azaryah were at sea on Shabbat. Rabbi Akiva and Rabbi Yehoshua chose to be strict on themselves and remain in a four-cubit space, whereas Rabban Gamliel and Rabbi Elazar ben Azaryah travelled the breadth of the boat: Eruvin 41b
Rabbi Akiva, Rabbi Yehoshua, Rabban Gamliel and Rabbi 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, Rabbi Elazar ben Azaryah and Rabbi Yehoshua cried about the happiness of Roman idolaters as compared to the destruction of the Temple, but Rabbi Akiva laughed, saying that those who follow Gd will be all the more rewarded, as compared to those idolaters: Makkot 24a-b
Rabban Gamliel, Rabbi Elazar ben Azaryah and Rabbi Yehoshua cried when they saw a fox walking in the former Holy of Holies, but Rabbi 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
Rabbi 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, Rabbi Yehoshua tried to change a certain legal practice. Rabbi 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
Rabbi Akiva called "Akiva" by Rabbi Yehoshua: Rosh HaShanah 25a; Makkot 24b
Rabbi Akiva reporting the practice of Rabban Gamliel and Rabbi Yehoshua, presumably to consider that as the correct practice: Succah 37b
Was Called "Bar Livai [Son of Levi]" by Rabbi Chanina: Shabbat 156a
Upset with Rabbi Elazar Chisma and Rabbi Yochanan Ben Beroka for not wanting to tell him Rabbi Elazar Ben Azaryah's statements from the Study Hall: Chagigah 3a
Rabbi Yehoshua Saying that a generation isn't orphaned if Rabbi Elazar Ben Azaryah lives in it: Chagigah 3b
Rabbi Yehoshua was expert in the laws of grafted produce; nonetheless, he went to Rabbi 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