His height: See here explaining his "Zuta" title on Ketuvot 69a
He was careful not to fall into any habits which could lead to Magic-Susceptibility: Shabbat 81b-82a
His and Rav Chisda's extra-legal lessons were well-known: Shabbat 89a
The method by which he cut fish, in his own special identifying symbol: Bava Metzia 23b
He was buried at the same time as Rav Hemnuna, and Rav Hemnuna's casket wouldn't enter a bridge until his did first: Moed Katan 25a-b
His Eulogy: Moed Katan 25b
Rava said that he prayed for humility like Rabbah bar Rav Huna's, and his request wasn't granted: Moed Katan 28a
Personal Practices
Yom Kippur Shoe: Yoma 78b, Yevamot 102b
The extent to which he went, to keep from having living creatures present during sexual relations: Niddah 17a
Placed a tablecloth over a meal which had been brought before Shabbat, in order to make Kiddush: Pesachim 100b
Measuring a tub on Shabbat [while sitting in it], without any purpose [MitAsek]: Shabbat 157b
Rescinding someone's vow, by asking him whether he would have vowed if ten people had been calming him down at the time of his vow, and receiving a negative response: Nedarim 21b
Interaction with Rav Chisda
Rav Chisda and Rabbah Bar Rav Huna against a witch, and using Magic for self-protection: Shabbat 81b-82a
Rav Chisda and Rabbah bar Rav Huna visiting Rav Nachman in a Succah which was valid only according to Rav Nachman, not because they gave in but because, as performers of the Mitzvah of visiting their Rebbe on the holiday, they were exempt from Succah: Succah 10b
Rav Chisda and Rabbah bar Rav Huna disagreeing with a ruling of Rav Huna's because they had not been told a reason, and Rav Huna responding, "Have you ever asked a reason and not been told it?": Succah 14b
Rav Chisda and Rabbah bar Rav Huna camping by the river in Sura overnight during Succot, on their way to visit the Exilarch: Succah 26a
Rav Chisda's and Rabbah Bar Rav Huna's Lessons on extra-legal Talmud were well-known: Shabbat 89a
Rabbah bar Rav Huna wouldn't go to Rav Chisda's Lesson, because Rabbi Chisda was teaching about bathroom-procedure, until his father told him to go: Shabbat 82a
Anecdotes Involving other Sages
Received judicial license from his father, Rav Huna: Sanhedrin 5a
Found Rav Pappa's father's donkey, and then tricked his character witnesses into saying that he was a Cheater; returned the donkey in the end: Bava Metzia 28b
His father, Rav Huna, once tore expensive clothing in front of him [in a way which could be repaired, although Rabbah was unaware], to test whether Rabbah would get angry: Kiddushin 32a
Rabbah bar Rav Huna saw that Rava [Rabbah] bar Rav Nachman was wearing a garment with Tzitzit-Fringes even though it was doubled up; he spread it out, showing that the fringes were actually in the middle, not at the corners: Menachot 41a
Rami bar Shemuel and Rav Yitzchak beraih deRav Yehudah, learning in the school of Rav Huna when overheard by Rav Huna's son, Rabbah bar Rav Huna: Niddah 17b
Rav Nechemiah breih d'Rav Yosef sending instructions to Rabbah bar Rav Huna Zuta in Neherdaa about collecting encumbered property from an estate for a woman's dowry: Ketuvot 69a