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 Nachman, Rav Chisda and Rav Sheshet were by the Exilarch on the second day of a two-day holiday, and a deer was brought which had been caught on the first day and slaughtered on the second day. Rav Nachman and Rav Chisda ate, reasoning that whichever day was the 'real' holiday, they were fine. Rav Sheshet refrained, holding that the days may be considered part of a single sanctity. Rav Sheshet then encountered Rabbah bar Shemuel and asked whether he had learned anything on the matter. When Rabbah bar Shemuel responded that they are two sanctities, Rav Sheshet said, "Don't tell them anything!" Rav Ashi reported, citing Ameimar, that the case was actually different, and that the last part involving Rabbah bar Shemuel never occurred: Eruvin 39b
Rafram interceding with the Exilarch on behalf of Raveina: Yoma 78a
Rav Hemnuna explaining the Mitzvah of changing clothing for Yom Kippur, to the Exilarch: Shabbat 119a
Rav Papi allowed the Exilarch's bakers to put dried, burnt grain into cooking food on Pesach: Pesachim 40b
Rav Nachman designed an entranceway [Tzurat haPetach] permitting transport in an alley on behalf of the Exilarch [Reish Galuta]. Rav Sheshet had a different opinion regarding its validity, and he told his assistant, Rav Gada, to remove it. The Exilarch's servants found Rav Gada and imprisoned him. Rav Sheshet stood by the prison gate and said, "Gada, Emerge!" Rav Gada emerged. Rav Sheshet later encountered Rabbah bar Shemuel and asked him whether he had anything to teach regarding entranceways, and Rabbah bar Shemuel taught that such an entrance would be valid. Rav Sheshet responded, "Don't teach that to the Exilarch's household! [I will recant on my own - Rabbeinu Chananel]": Eruvin 11b
Rav Nachman implemented a controversial business deal for the Exilarch, and Rav Yehudah tore up the document. In one version, Rav Nachman respected Rav Yehudah's challenge. In another version, Rav Nachman dismissed Rav Yehudah and all other challengers in financial law as 'children': Bava Metzia 66a
Rav Nachman permitted a woman from the Exilarch's household to re-marry after her husband died even though she had a child who needed nursing, because she arranged for a nursemaid and Rav Nachman knew that no one would back out on the Exilarch. He didn't permit it for others: Ketuvot 60b
The Exilarch asked Rav Huna bar Chinina to fix up a shady area in such a way that it would be usable for Shabbat. Rav Huna bar Chinina made arrangements, which Rava took apart, as he felt they were unnecessary. Rav Pappa and Rav Huna breih deRav Yehoshua removed the materials, so that Rav Huna bar Chinina could not re-establish his arrangement, but they then realized on Shabbat that he had been correct. The Exilarch cited a verse regarding Rav Pappa and Rav Huna breih deRav Yehoshua - "They are wise to perform evil, but they don't know how to do good": Eruvin 25b-26a
Ulla reported that the Elders of the South presented a law, and the Reish Galuta shouted ["taka"] at them in his retort: Zevachim 22b-23a
Specific Oppresive Governments
The difference between the Arami and Persian oppressions: Gittin 17a
Either the Jews or Edomites will be on top, but never both: Pesachim 42b
Hashem having the angel Gavriel punish Rome in the time of the Messiah, because they devoted themselves to destroying the Jews: Pesachim 118b
Disruption of the holiday celebrations in Israel [unintentionally] by the tax collectors: Shabbat 145b
One may not fast on the 28th of Adar, because on that date Yehudah ben Shamua and his peers succeeding in preventing a decree which would have been against teaching Torah, circumcising, and keeping Shabbat: Rosh HaShanah 19a