Generally speaking, when one hears the Name of G-d recited as part of a Beracha, he answers, "Baruch Hu U’Baruch Shemo."

Under certain circumstances, however, one should not answer "Baruch Hu U’Baruch Shemo" upon hearing a Beracha. At any point in the prayer service from "Baruch She'amar" until after the Amida, one may not interrupt to answer "Baruch Hu U’Baruch Shemo." Therefore, if, for example, as a person recites Ashrei he hears somebody recite the Beracha over his Tallit, he should not respond with "Baruch Hu U’Baruch Shemo" upon hearing G-d's Name.

The exception to this rule is if somebody hears a Beracha after he completed the Yishtabach paragraph but before he began the next section, of Yotzer. If one completed reciting the final words of Yishtabach ("Melech Yachid Kel Chai Ha'olamim"), but has yet to begin the Beracha of Yotzer, he may – and should – answer "Baruch Hu U’Baruch Shemo" upon hearing G-d's Name in a Beracha.

During Birkat Kohanim (the priestly blessing), one should softly answer "Baruch Hu U’Baruch Shemo" each time he hears the Chazan call out G-d's Name. Of course, after each of the three sections of Birkat Kohanim, one should respond with "Amen" in a loud voice. Many people unfortunately do not pay proper attention during Birkat Kohanim and are neglectful with regard to these responses.

One does not recite "Baruch Hu U’Baruch Shemo" when listening to a Beracha through which he fulfills his obligation to recite it. For example, if one fulfills his obligation of Kiddush or Havdala by listening to its recitation by somebody else, he should not answer "Baruch Hu U’Baruch Shemo" upon hearing G-d's Name in the Beracha. Other examples are the Beracha recited over Shofar blowing and the Beracha recited before the reading of the Megila. In all these and similar instances, when one fulfills his obligation by listening to a Beracha's recitation, he does not answer "Baruch Hu U’Baruch Shemo."

Another example, of which many people are unaware, is the blessings recited under the canopy at a wedding. The blessings recited by the Chazan or Rabbi during the ceremony are essentially recited on behalf of the bride and groom, and they must therefore listen attentively to these Berachot. (Many brides and grooms pray during the recitation of these blessings, which is incorrect.) The bride and groom should not respond with "Baruch Hu U’Baruch Shemo" upon hearing G-d's Name in these Berachot; they should rather listen silently and answer "Amen" when the Beracha is completed.

Nevertheless, if one mistakenly answers "Baruch Hu U’Baruch Shemo" when listening to a Beracha through which he fulfills his obligation with regard to that Beracha, he has, indeed, fulfilled his obligation. Although one optimally should not answer "Baruch Hu U’Baruch Shemo" in these situations, doing so does not, after the fact, undermine his fulfillment of his obligation. So long as both he and the person reciting the Beracha had in mind that he fulfills his obligation through this recitation, he satisfies his obligation, even if he mistakenly answers "Baruch Hu U’Baruch Shemo."

Summary:

1) Generally speaking, one answers "Baruch Hu U’Baruch Shemo" upon hearing G-d's Name as part of a Beracha.

2) One does not answer "Baruch Hu U’Baruch Shemo" if he is anywhere in between Baruch She'amar and the end of the Amida, unless he has completed Yishtabach and has yet to begin the Beracha of Yotzer.

3) When one hears the Chazan call out the Name of G-d in Birkat Kohanim, he should softly answer "Baruch Hu U’Baruch Shemo."

4) One should not answer "Baruch Hu U’Baruch Shemo" when he listens to a Beracha through which he fulfills an obligation; if, however, he mistakenly does answer "Baruch Hu U’Baruch Shemo," he has nevertheless fulfilled his obligation.