Shacharis: Once Barchu is recited, it is forbidden to talk until after completing Shemone Esray. After completing the silent Shemone Esray, it is forbidden to speak if it will disturb others who are still davening. During the Repetition of the Shemone Esray it is forbidden to speak. After the Repetition of the Shemone Esray is completed, a person should not talk as Shemone Esray should be connected to Tachanun. At the end of davening (Ashrei, Uva L’sion, Aleinu, and Shir Shel Yom), there is no prohibition to talking but a person should still refrain from talking (as this could be a disturbance to others). Also, any conversation must be considered appropriate for the shul.
(laws of talking during Krias Ha’Torah will be discussed a different week)