Gemara

Rava: We learn great Halachos from the custom of how we say Hallel...

The Shali'ach Tzibur says "Baruch ha'Ba", and the Tzibur answers "b'Shem Hash-m". This teaches that Shome'a k'Oneh.

Question: If one heard but did not answer, what is the law?

Answer (R. Chiya bar Aba): Chachamim, Sofrim, the heads of the nation and those who expound all say that he was Yotzei.

Support - Question: "Es Kol Divrei ha'Sefer Asher Kora Melech Yehudah" - Yoshiyahu (Melech Yehudah) did not read them, rather, Shofan did - "Va'Yikra'ehu Shofan Lifnei ha'Melech"!

Answer (R. Shimon ben Pazi): This teaches that Shome'a k'Oneh.

Berachos 47a - Rabah bar bar Chanah: The one who blesses ha'Motzi may not cut the bread until those who will be Yotzei with his Berachah finish answering Amen.

Rav Chisda: He must wait for the majority to answer Amen.

Rami bar Chama: This is because Amen is considered part of the Berachah.

51b - Mishnah: We answer Amen after a Yisrael's Berachah. One does not answer Amen to a Kusi's Berachah unless he heard the entire Berachah.

53b - Inference: One answers Amen after a Yisrael's Berachah even if he did not hear the entire Berachah.

Question: If he did not hear it, he cannot be Yotzei with it!

Answer (Chiya bar Rav and Rav Nachman): This is when the Oneh (the one who answers) does not need not be Yotzei.

54b: Rav Yehudah fell sick and recovered. R. Chana Bagdata'ah and Rabanan visited him and said "Blessed is the merciful One who gave you to us, and not to the dirt"!

Rav Yehudah: You exempted me from thanking (blessing ha'Gomel).

Question: But Abaye taught that one must bless in front of ten people!

Answer: There were ten people there.

Question: But Rav Yehudah himself did not bless!

Answer: (It sufficed that) he answered Amen.

Rishonim

Rif and Rosh (3:28): If one heard but did not answer, he was Yotzei.

Rif and Rosh (Berachos 43a and 9:3): Rav Yehudah was Yotzei because he answered Amen to them.

R. Yonah (DH Omar): It seems that even if there were not 10 people and the Choleh would not be Yotzei, the others are permitted to make the Berachah.

Rambam (Hilchos Berachos 1:11): If one heard a Berachah from the beginning to the end and intended to be Yotzei, he was Yotzei even if he did not answer Amen. If one answers Amen to a Berachah it is as if he blessed himself, if the Mevarech (the one who blessed) was obligated to make the Berachah. If one is obligated mid'Oraisa to make a Berachah, he can be Yotzei through listening only if the Mevarech was also obligated mid'Oraisa.

Question (Kesef Mishneh): The Gemara discussed one who answered Amen, and asked how he can be Yotzei if he did not hear the entire Berachah. This shows that even one who answers must hear the entire Berachah to be Yotzei. Why does the Rambam say that if one answers Amen, it is as if he blessed himself? He is Yotzei even if he did not answer!

Answer #1 (Kesef Mishneh): One who did not answer Amen was Yotzei, but it is not as if he himself blessed.

Answer #2 (Kesef Mishneh): The Rambam teaches that even if one answered Amen, he was Yotzei only if the Mevarech was obligated to bless.

Einayim l'Mishpat (Berachos 45b:2): It seems that according to Answer #1, one who did not answer Amen is Yotzei due to Arvus (mutual responsibility of Yisraelim for each other). If one answers Amen, it is as if he himself blessed. Even though Shome'a k'Oneh, l'Chatchilah one must answer.

R. Yonah (Berachos 13b DH v'Yesh): All agree that we do not interrupt Shemoneh Esreh to answer to Kaddish. Rabbeinu Yakov says that one may not pause to hear the Tzibur answer "Yehei Shemo ha'Gadol Mevorach", for Shome'a k'Oneh, so this is like interrupting. Rav Hai Gaon and the Rif say that since this is a praise of Hash-m, it is not considered an interruption.

Tosfos (Berachos 21b DH Ad): R. Tam and the Ri say that if Shome'a k'Oneh, listening is an interruption! However, one may rely on the custom to answer.

Poskim

Shulchan Aruch (8:5): If several people put on Taleisim at the same time, each blesses for himself. If they want, one may bless and the others answer Amen.

Gra (DH veha'Acherim): B'Di'eved they are Yotzei even if they did not answer Amen.

Shulchan Aruch (25:10): If someone heard Kaddish or Kedushah between Tefilin Shel Yad and Shel Rosh, he does not answer. He listens and has intent for what they say.

Beis Yosef (DH u'Mah she'Chosav): The Rashba holds that one who listened must make another Berachah afterwards, for Shome'a k'Oneh, and it is an interruption. He similarly forbids to listen during Shemoneh Esre. We hold that one may listen during Shemoneh Esre, or between Tefilin Shel Yad and Shel Rosh. Shome'a is k'Oneh to be Yotzei a Chiyuv, but not to be considered an interruption.

Shulchan Aruch (594:1): If Reuven did not pray nine Berachos (of Musaf of Rosh Hashanah), Shimon cannot be Motzi him.

Kaf ha'Chayim (3): Shimon can be Motzi him only if nine answer Amen to his Berachos, for then it is considered Tefilah b'Tzibur.

Shulchan Aruch (OC 213:2): One who blesses (on food) is not Motzi others unless he eats or drinks with them. Then they are Yotzei by listening if they have intent, even if they do not answer Amen.

Mishnah Berurah (15): If he does not eat with them, his Berachah is l'Vatalah, so surely they are not Yotzei. However, if he did not eat with them due to Shogeg or Ones (e.g. his wine spilled), they are Yotzei.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): According to the opinion that does not require intent for Mitzvos, they are Yotzei even if they did not intend and the Mevarech did not intend to Motzi them.

Mishnah Berurah (17): Even if one did not answer Amen, Shome'a k'Oneh and it is as if he blessed himself. One must answer Amen to any Berachah he hears from a Yisrael. There is a bigger obligation when he wants to be Yotzei to answer, to actively show that he agrees with the Berachah.

Kaf ha'Chayim (21): One must be careful to answer Amen when he is Yotzei, for it is considered part of the Berachah. The Yerushalmi says that one who answers Amen should have in mind to be Motzi the Mevarech

Shulchan Aruch (219:4): If Reuven said (in front of Shimon) 'Baruch Atah Hash-m...that bestowed all good to you', and Shimon answered Amen, he was Yotzei.

Source (Tur, citing the Rosh): One is Yotzei without answering only if the Mevarech was obligated to bless. According to this, if Reuven blessed ha'Gomel for himself, and Shimon heard and had intent to be Yotzei, he was Yotzei even if he did not answer Amen.

Question (Drishah 2): Why does the Tur say 'according to this'? The Tur already wrote (213) that one who blesses on food is Motzi others only if he eats with them, whether or not they answer Amen!

Note: Perhaps we would have thought that one must always answer Amen to be Yotzei ha'Gomel, e.g. for the reason of R. Akiva Eiger (below), or to publicize his gratitude.

R. Akiva Eiger: Here Shome'a k'Oneh does not apply, for Shimon must say a different text, '...that bestowed all good to me.' By saying Amen, he shows that he agrees with the praise. However, this is unlike the Tur.

Sha'ar ha'Tziyon (8): The Ro'oh argues, and says that one is Yotzei by merely listening. The Gemara did not really mean that he must answer Amen to be Yotzei.

Kaf ha'Chayim (31) We require that Reuven intended to be Motzi Shimon.

Note: Rav Yehudah told R. Chana Bagdata'ah and Rabanan that they were Motzi him. We must say that they intended to be Motzi him. If so, there was no need to tell them! Perhaps only some of them intended, and he needed to tell the others. Alternatively, he meant 'if you had intent, you exempted me'.

Rema: Even though Reuven was not obligated to bless, since he blesses to praise Hash-m for the good that He did to Shimon, it is not a Berachah l'Vatalah.

Shulchan Aruch (219:5): If Reuven blessed ha'Gomel for himself and intended to be Motzi Shimon, and Shimon heard and had intent to be Yotzei, he was Yotzei even if he did not answer Amen.

Rema: Since Reuven was obligated to bless, Shimon was Yotzei without answering.

Shulchan Aruch (OC 141:2): If the Shali'ach Tzibur reads aloud, the Oleh may not. However, he must read quietly, or else his Berachah is l'Vatalah.

Beis Yosef (DH u'Mitoch): If the Oleh hears every word from the Shali'ach Tzibur and has intent, it is as if he said it, for Shome'a k'Oneh.