Rami bar Chama's sister married Rav Avya, and her ketubah was lost: Ketuvot 56b-57a
Series of questions: Menachot 68b-69a
Rami bar Chama asking a question with an obvious answer, and the Gemara commenting that he had not been careful with his words, due to the speed of his thought process; he had meant to ask a similar, more difficult question: Eruvin 90a
Rav Bibi bar Abbaye asked a question, which sounded like Rami bar Chama's question. Rav Bibi responded, "Would I argue based on someone else's question?! Rather, I mean...": Eruvin 90a
Rami bar Chama's host had a problem with a transaction, and Rami bar Chama sent him to Rav Nachman for a ruling: Bava Metzia 51a
Rami bar Chama said of Rabbi Oshia son of Rabbi Chama bar Bissa, "The tripled-threaded cord will not swiftly be severed" (from Kohelet 4): Ketuvot 62b