The importance of proper reading of a prayer, with the proper pronunciation etc, aside from proper intent: Succah 39a
The righteous are those who arrive early and leave late for prayer: Megillah 15b
Requirement to prepare one's Prayer: Rosh HaShanah 35a
Concentration during Prayer
Reward for examining one's prayer: Shabbat 118b, 127a
Praying while one is intoxicated, at different stages of intoxication: Eruvin 64a-65a
The prayer of a truly intoxicated person is an abomination: Eruvin 64a
If a person skips prayer because he is intoxicated, Gd will prevent troubles from befalling him: Eruvin 65a
Prayer while one's mind is not settled: Eruvin 65a
Prayer while one is angry: Eruvin 65a
Prayer during the first three days after one returns from a long trip: Eruvin 65a
Prayer in a house where there are strong smells, as from alcohol or fish: Eruvin 65a
Whether insincere prayer will be accepted: Taanit 8a
Goals of Prayer
Elisha the Prophet performed his miracles via prayer: Megillah 27a
Prayer is always good for a person [besides prayer which will affect Gd's verdict]: Rosh HaShanah 16a, 18a
Prayer can overturn Gd's Judgment: Rosh HaShanah 16b
Requirement to pray for another's benefit, especially for a Torah Scholar: Berachot 12b
Prayer on behalf of a wicked person: Berachot 10a; Eruvin 41b
Praying on behalf of a person who is forced to sin by Gentiles, temporary insanity, or poverty: Eruvin 41b
One should not pray after an event has already occurred, because that is considered a pointless prayer: Bava Metzia 42a
How we know that one should pray for rain: Taanit 2a
We don't pray for two crises at once, such as plague and drought: Taanit 8b
Value of Prayer
It would be good [and not a wasted Blessing] if people prayed all day: Berachot 21a; Pesachim 54b
The Mitzvah of Prayer is considered to stand at the "Height of the World": Berachot 6b (See Rashi)
Prayer is considered "Tzedek" [righteousness]: Berachot 14a
Prayer takes the place of Temple offerings - "U'Neshalmah Parim Sefateinu": Yoma 86b
Prayer is appropriate from a person who is able to praise all of HaShem's aspects: Makkot 10a
The power of the prayer of the righteous: Succah 14a
The importance of relying on Gd, and not on humanity: Megillah 15b
Gd only hears a person's prayer if his heart is soft/gentle like flesh: Sotah 5a
If a person is humble, it is as though he has brought all of the Temple offerings, and his prayers will never be rejected: Sotah 5b
There is a greater level in praying on time than in praying at one's choosing: Berachot 26a
Since the destruction of the Beit haMikdash, the gates of prayer are closed, but the gates of tears remain open: Bava Metzia 59a