Ga'al Yisrael - Answering Amen
There is much discussion as to whether or not one is permitted to respond "amen" to the leader's conclusion of the "ga'al yisrael" blessing recited before the Shemoneh Esrei of shacharit. The difference of opinion is based on the fact that one is required to be "somech geula l'tefilla", to "connect redemption to prayer". What this means is that the blessing of "ga'al yisrael" ("redemption") must immediately precede the Shemoneh Esrei ("prayer") with no interruption whatsoever. Even remaining silent and motionless is deemed to be an interruption for this purpose. As such, it is a matter of dispute among halachic authorities whether it is permitted to respond "amen" between "ga'al yisrael" and the Shemoneh Esrei or that too constitutes an unnecessary interruption and is forbidden.
Ensuring to begin the Shemoneh Esrei immediately after reciting the blessing of "ga'al yisrael" is actually of great consequence. For example, the sages teach us that one who is careful to do so is assured a place in the World to Come. The source for the requirement to connect "redemption" and "prayer" is derived from the book of Tehillim where a verse referring to "redemption" immediately precedes one referring to "prayer". It is interesting to note that some authorities rule that the requirement not to interrupt between "ga'al yisrael" and the start of the Shemoneh Esrei does not apply on Shabbat. Others disagree and rule that no interruption should be made on Shabbat, either.
As such, most authorities forbid one who is about to begin the Shemoneh Esrei to respond "amen" to the leader's recitation of "ga'al yisrael", deeming it to be a forbidden interruption. Other authorities permit and even encourage one to do so, arguing that this "amen" is not an interruption between "ga'al yisrael" and the start of the Shemoneh Esrei, but rather an essential component of it. Although one who has an established custom regarding answering "amen" at this point in the prayers should conduct himself accordingly, there are a number of solutions which have been suggested in order to avoid this dispute entirely.
One of these suggestions is to pause when reaching the words "shira chadasha" or "tzur yisrael". One then waits for the leader to conclude the "ga'al yisrael" blessing at which time one responds "amen", as doing so is permitted at that point in the prayers. One then resumes praying thereby commencing one's silent shemoneh esrei several seconds thereafter. Conducting oneself in this manner allows one to both connect "ga'al yisrael" to the Shemoneh Esrei, as well as answer "amen" to the leader's blessing. This solution has not found widespread acceptance, however, as it precludes one from beginning the Shemoneh Esrei simultaneously with the leader and everyone else in the congregation, which is to be preferred.
Another option is to pace oneself in order that one concludes the blessing of "ga'al yisrael" at the exact same time as the leader. Doing so exempts one from having to respond "amen" entirely. This is because one generally does not respond "amen" when concluding a blessing at the same time as someone else. One may also conclude "ga'al yisrael" a second or two before the leader and then begin the introductory words of the Shemoneh Esrei, "Adonai sefatai". In this manner one avoids the issue entirely as all authorities agree that once one has begun the Shemoneh Esrei, even if only the introductory words, answering "Amen" is prohibited.
Similarly, one can pace oneself so that one is a few words behind the leader. As such, when the leader recites "ga'al yisrael" one will be in the midst of "baruch ata adonai" at which time one is not permitted to answer "amen" anyway. One can then conclude one's blessing and begin the Shemoneh Esrei without interruption. This option seems to be the most preferred.
Finally, there exists a widespread, though somewhat halachically problematic, solution to the issue and that is to simply have the leader conclude the "ga'al yisrael" blessing silently. In such a situation, there would be no requirement to answer "amen" because one may not answer "amen" to a blessing that one has not heard. This approach, however, is problematic and questions the legitimacy of the entire service as well as the one leading it. This is because the sages decreed that it is essential that the one leading the prayers make himself heard by the entire congregation especially when concluding a blessing. Indeed, it seems that this approach, though quite widespread, is without solid halachic basis.
In ancient times the entire service was recited out loud for the benefit of those who may not know how to pray on their own. The original enactment of reciting at least the conclusion of the blessings out loud remains in place even though today most people are able to pray on their own. It is also deemed disrespectful towards the blessing itself to recite a part of it out loud and a part of it silently.
There are a number of contemporary authorities who are noted for their exceptionally strong objection to the practice of concluding "ga'al yisrael" silently. Nevertheless, there are a number of authorities who do justify the practice as a way of saving oneself from having to answer "amen" at a point in the prayers when doing so is problematic. One who does not have a custom to the contrary should always recite "ga'al yisrael" out loud when leading services.