Amen
One who hears another person recite a blessing is required to respond "amen" to the blessing.[1] In fact, in addition to there being a scriptural source for the requirement to answer "amen" to the blessings recited by others, it is also a practice which was specifically decreed by Moshe Rabbeinu, as well.[2] It is taught that the word "amen" is an acronym for the words "El Melech Ne'eman" – God is a faithful King. It is also a derivative of the word "emuna" meaning "faithful" or "true," referring to the intentions that one should have in mind when responding "amen" - that the blessing just recited is indeed true and fitting.[3] One is even required to respond "amen" to a blessing recited by a non-Jew.[4]
The sages teach us that anyone who answers "amen" with all their might will have the doors of Heaven opened for them.[5] Furthermore, we are taught that the one who responds "amen" to a blessing receives more reward than the one who actually recited it.[6] A child who answers "amen" to a blessing already assures himself a place in the World to Come.[7] According to kabbala, it is meritorious to ensure that there always be another person present when one recites a blessing, in order to allow for an "amen" response to be attached to it.[8] One should not respond "amen" in a louder voice than the one who recited the blessing.[9]
A blessing need not contain the name of God in order to warrant responding "amen".[10] For example, one is encouraged to respond "amen" even when someone merely wishes you well.[11] Although one not need hear the entire blessing in order to respond "amen", one must, however, be aware of which blessing was recited.[12] One who responds "amen" to a blessing can be included in the effects of the blessing without having to personally recite the blessing. For example, common custom is for all who are present at a Shabbat meal to partake of the challa bread after simply responding "amen" to the blessing recited by the master of the house. This is because when one pays attention to the recitation of a blessing and responds "amen" it is considered as if one had actually recited the blessing oneself.[13]
One does not respond "amen" to a blessing heard on a tape or radio.[14] One may respond "amen" to a blessing heard over the telephone[15] though one is not obligated to do so.[16] Neglecting to respond "amen", even to the blessing of a minor, is a serious offence for which one will be called upon to make an accounting.[17] An "amen" should not be said in response to an unnecessary or unwarranted blessing.[18] One must be careful to promptly recite "amen" when hearing a blessing though one must be sure not to say it until the blessing has been recited in its entirety.[19]
On a related note, it is said in the name of Rabbi Eliyahu Lopian and Rabbi Simcha Broide that it would have been worth Hashem's while to create the entire universe just in order for a single Jew to be able to respond "baruch hu u'varuch shemo" a single time. Moreover, one thousand responses of "baruch hu u'varuch shemo" don't amount to the power of even one "amen." Furthermore, one thousand amens don't amount to even one "amen yehei shemei rabba." Finally, one thousand responses of "amen yehei shemei rabba" don't equal the study of even a single word of Torah.
[1] O.C. 215:2
[2] Mishna Berura 215:8
[3] Shabbat 119b, Ta'anit 16b
[4] Rema O.C. 215:2
[5] Shabbat 119b
[6] Berachot 53b
[7] Rema O.C. 124:7
[8] Kaf Hachaim 124:31
[9] O.C. 124:12
[10] Mishna Berura 215:9, Shulchan Aruch Harav 189:6, 215:2
[11] Piskei Teshuvot 215:7
[12] Shulchan Aruch Harav 124:11, 215:2
[13] Rambam Berachot 1:11
[14] Rivevot Ephraim 6:93
[15] Shaarei Halacha U'minhag (Chabad) Vol. 1 p. 166
[16] Piskei Teshuvot 215:3
[17] Chayei Adam 6:1
[18] Rambam Berachot 1:15, O.C. 215:4
[19] Rambam Berachot 1:14, O.C. 124:8