Hi @Michael this is quite a wide-reaching question.
The following is not definitive but hopefully a good start. People can feel free to turn this answer into a Wiki and add to it.
Bava Metziah 86b - lists Michael, Gavriel, and Raphael who visted Avraham
Yoma 37a - Also reference to three above
Berachos 4b - Hierarchy of angels based on flight incl. Michael, Gavriel, Eliyahu and Malach Hamaveis
Berachos 4b - Comparing Michael and Gavriel
Megilla 12b - Gavriel fashioning a tail for Vashti
Sanhedrin 21b - Gavriel's action following Shlomo marrying Pharoah's daughter
Sotah 33b - Gavriel teaching Yosef 70 languages
Pesachim 118b - Hashem speaking to Gavriel
Menachos 29a - Gavriel's belt
Sanhedrin 95b - Hashem speaking to Gavriel about his scythe
Zevachim 62a, Menachos 110a & Chagigah 12b - Michael offering sacrifices on altar in shamayim
Avoda Zara 42b - lists Michael as part of list of things that one slaughters an animal for in order to worship which is forbidden to do
Yoma 77a - Conversation between Hashem and Michael
MALACH HAMAVEIS (MH)
Shabbos 30b - MH killing David Hamelech
Bava Basra 16a - Satan and MH being one
Shabbos 89a - Talks about how all the angels came to admire Moshe for arguing why humans should receive the Torah and even the MH gave something
Avoda Zara 5a - The Jewish people accepted the Torah only in order that the Angel of Death would not rule over them
Avoda Zara 20b - first talks about not to look at animals mating and how even if one were like the MH who is full of eyes, a person shouldn't look and then later, the way the MH kills humans
Yoma 77b - MH doesn't have permission to pass through river that will in future flow from the Holy of Holies
Bava Metziah 36b - The reason that a person liable to pay is because even if the Angel of Death spared the life of the animal, it would be standing in the house of the thief due to the negligence of the bailee.
Avoda Zara 35b - MH love for talmud chacham
Chullin 35b - It was necessary for Rabbi Shimon to teach the halacha of blood of the animal that is dead as a result of natural causes, as it could enter your mind to say: What difference is there to me if one killed the animal himself, and what difference is there to me if the animal was killed by the angel of death?
Bava Kamma 60b - If there is a plague in the city, a person should not enter the shul alone, as the Angel of Death leaves his utensils there