Right Hand Over Left
When praying the Shemoneh Esrei one should place his hands upon his heart, the right hand on top of the left; standing with fear and awe like a servant before his master. (Shulchan Aruch 95:3)
The source of the above ruling is found in the Rambam's Mishneh Torah (Laws of Prayer 5:4). There is a dispute among the later Rabbis as to whether this ruling is based on the Rambam's own opinion, and is therefore the result of the custom of his time and place (Rabbi Yitzchak Abuhav, Bach), in which case this rule would be dependent on the accepted custom in each different place; or if this ruling is based on the gemara in Shabbat 10a, in which case one could contend that the rule would be consistent in all places (Beit Yosef). The latter opinion appears to be the ruling of the Shulchan Aruch as quoted above.
Many of the later authorities, however, rule in accordance with the first opinion. They explain that the proper way to stand during the Shemoneh Esrei is based on the accepted custom of how one stands before a king (and the like) in each place (Magen Avraham, Shulchan Aruch HaRav, Mishneh Berurah). Thus, the Aruch HaShulchan writes (Orach Chaim 91:6), “Each person is different; for some it is difficult to pray like this (hands over the heart), and instead they place their hands on a shtender. Each person should do whatever is best for him in order to pray.” Accordingly, many people do not place their hands on their hearts.
The Mishneh Berurah writes in the name of Asarah Ma'amarot that the Arizal would place his arms on his heart, the right hand on top of the left. Similarly, the Kaf HaChaim quotes the writings of the Arizal (Sha’ar Hakavanot), where it is explained that the correct way to stand during the Shemoneh Esrei according to Kabbalah is as explained by the Rambam and the Shulchan Aruch. He further explains that according to the Arizal this rule is not dependent on the custom of how one stands before a king in the different parts of the world.
The Darchei Moshe, based on Kabbalah, explains that the reason why the right hand should be placed on top of the left is in order to “strengthen” the Divine attribute of rachamim (mercy) over din (strict judgment). This explanation is also taught in the writings of the Arizal. It is important to note that the Rema (author of Darchei Moshe) did not see the writings of the Arizal, as these writings did not reach Europe until later.