Gemara

(R. Yehoshua ben Levi): If one answers 'Amen Yehei Shmei Raba' with all his Ko'ach (concentration), harsh decrees against him are torn up

Berachos 21b: All agree that we do not interrupt Shemoneh Esreh to answer to Kedushah.

Question: Do we interrupt Shemoneh Esreh to answer "Yehei Shemo ha'Gadol Mevarach" (in Kaddish)?

Rishonim

Rambam (Seder Tefilos (b'Sof Hilchos Tefilah), Nusach ha'Kaddish): Chachamim commanded to answer Amen Yehei Shmei Raba with all one's Ko'ach.

R. Yonah (13a DH b'Chol): One answers with all his Ko'ach, i.e. all Ko'ach of his Kavanah. Some people's Kavanah is aroused only through Ko'ach, therefore it says b'Chol Kocho. One need not make great noises that people will mock.

Beis Yosef (DH a'Ha): Rashi explained similarly in Shabbos. Tosfos (119b DH Kol) cites a Medrash that says that when Yisre'elim enter Batei Kenesiyos and answer Amen Yehei Shmei Raba in a great voice, this annuls harsh decrees. It seems that one must answer in a loud voice. The Zohar says so.

Maharsha (Shabbos 119b DH b'Chol): When one answers 'Amen Yehei Shmei Raba', Hash-m uses all His Ko'ach ("Yigdal Na Ko'ach Hash-m" - Bamidbar 14:17) to tear harsh decrees against him.

Poskim

Shulchan Aruch (OC 56:1): One should have intent when answering to Kaddish.

Magen Avraham (1): Be'er Sheva (31) says that the Gemara asked whether one may interrupt (Shemoneh Esre) to say Yehei Shmei Raba, but it did not ask about interrupting for Modim or Kedushah, for surely one does not interrupt for them. This shows that Amen Yehei Shmei Raba is greater than Kedushah and Modim.

Mishnah Berurah (1): If one answers 'Amen Yehei Shmei Raba' will all his Ko'ach, i.e. concentration, heart and soul, harsh decrees against him are torn up. He must hear the Kaddish from the Shali'ach Tzibur to know to what he answers. All the more so he must be careful not to talk during Kaddish or Kedushah. One may not even think about Torah at the time.

Mishnah Berurah (2): The Shali'ach Tzibur should say bi'Zman Kariv v'Imru Amen at once without pausing, for the custom is not to answer until he says Amen. If the Shali'ach Tzibur sings this at length, one should not wait. (Rather, he answers after Kariv.) One pauses slightly between Amen and Yehei Shmei Raba, and similarly between Amen and Modim, for Yehei Shmei Raba is a separate matter.

Shulchan Aruch (ibid.): One answers it in a great voice, and strives to run in order to hear Kaddish.

Magen Avraham (3) and Mishnah Berurah (7): One should not be so loud that people will mock him, for he causes them to sin.

Nezirus Shimshon: Why did the Magen Avraham bring this from R. Yonah? He holds that Kol Kocho means 'all his Kavanah.' The Beis Yosef rules like the Zohar and Tosfos, who say that it means in a loud voice!

Mishnah Berurah (124:47): One answers Amen or Borchu as loud as the one who blessed, but no louder, unless he must arouse others to answer.

Halichos Shlomo (6:15(50)): Amen Yehei Shmei Raba is an exception to this rule. It seems that the Mishnah Berurah agrees, for he forbids only if one is so loud that people will mock him.

Kaf ha'Chayim (15): One may not answer louder than the one who says Kaddish.

Mishnah Berurah (6): If there are many Minyanim nearby, and he hears Kaddish from two of them at once, he answers [once]. One may not interrupt Amen Yehei Shmei Raba to answer Kedushah. It is not clear whether one may interrupt Kedushah to answer Amen Yehei Shmei Raba.

Kaf ha'Chayim (6): One does not interrupt Kedushah to answer Amen Yehei Shmei Raba.

Kaf ha'Chayim (5): If one already heard Kaddish but did not answer Kedushah, it is better to [go to a Beis ha'Keneses where he can] answer Kedushah, for it is good to fulfill both of them. If one is obligated to hear this Kedushah, e.g. during Chazaras ha'Shatz after he prayed, and he hears Kaddish from elsewhere and he can answer only to one of them, Kedushah had precedence, for this is its proper time.

Kaf ha'Chayim (8): If one hears two Kaddeshim at once, if they are separated by less than Kedei Dibur (the time to say three or four words), he answers to the first or last. If they are separated by Kedei Dibur, he answers to each one.

Kaf ha'Chayim (10): Yalkut Reuveni brings a Medrash that says that an angel ties crowns for Hash-m from Kaddish, Borchu and Amen Yehei Shmei Raba that Yisrael answer. Therefore, one who omits them diminishes Hash-m's crown, and he is Chayav Niduy (excommunication) until he will bring a Korban in the future.

Kaf ha'Chayim (18): If only people would strive as much to answer to Amen and Kaddish as they do in order to gain money!

Rema: One should stand when answering to Kaddish and every Devar shebi'Kedushah.

Magen Avraham (4): Hagahos Minhagim brings this from the Yerushalmi. Darchei Moshe says that the Maharil would not stand for Kaddish, unless he was standing beforehand, e.g. in Kaddish after Hallel. The Ari Zal did similarly. He said that there is a printing mistake in the Yerushalmi. Yonas Elem says that whether the Yerushalmi says that Eglon was commanded to stand to hear Devar Hash-m, or he stood on his own, all the more so a Yisrael should stand!

Chasam Sofer: If we learn from the verse that one must stand, this is a Mitzvah from Divrei Kabalah (Nevi'im), and it applies even if he had a Mitzvah to sit, e.g. during Tachanun or Birkas Yotzer Ohr. If we learn from a Kal va'Chomer, we cannot learn more than the source (Eglon had no Mitzvah to sit), and it does not apply when there is a Mitzvah to sit.

Mishnah Berurah (7): One stands until finishing Amen Yehei Shmei Raba. Some say to stand until "v'Imru Amen" after d'Amrin b'Alma.

Mishnah Berurah (8): Some say that one need not stand, unless he was standing beforehand. One should be concerned for the stringent opinion. If a Nochri king stood for Hash-m's word, all the more so we, His nation, should!

Kaf ha'Chayim (21): If one stood to honor a Zaken (old person or Chacham), he must remain standing for Kaddish. However, if he did not fully rise, rather, he rose a little to show honor, he need not stand for Kaddish.

Rema (ibid.): If one comes to the Beis ha'Keneses and hears the Tzibur answering Kaddish, he answers with them, even though he did not hear the Shali'ach Tzibur say Yisgadel...

Magen Avraham (5): One answers Yehei Shmei Raba with them. If he can think (what the Shali'ach Tzibur must have said) and intend to answer to it, he says also Amen (before Yehei Shmei Raba).

Gra (DH u'Mi): Yehei Shmei Raba is a separate praise (from the first part of Kaddish). Also, the theme of Kaddish was not yet finished. Therefore, this is unlike answering an orphaned Amen (i.e. when one did not hear to what he answers, or paused before answering).

Mishnah Berurah (9): If one finds the Tzibur at the end of 'Amen Yehei Shmei Raba...', he answers only 'Yehei Shmei Raba', for this is an independent praise, but not Amen. If he entered while the Tzibur is saying 'Amen Yehei Shmei Raba...', and he can intend for what they answer to, he says also Amen Yehei Shmei Raba.

Note: One must answer within Toch Kedei Dibur of the Berachah, or while most of the Tzibur is still answering. If one heard Amen Yehei, this is four words from bi'Zman Kariv, to which he answers Amen! We must say that onemay answer if he speaks slower than the Tzibur. It is within the time he takes to say two or three words.

Kaf ha'Chayim (26): One may answer as long as the Tzibur did not finish answering.

Rema (ibid.): Also the Shali'ach Tzibur must be careful to say Yehei Shmei Raba.

Mishnah Berurah (2): The Shali'ach Tzibur says Yehei Shmei Raba quietly.