What is this Pasuk coming to teach us?
Rashi #1: 'When I recite the Name of Hashem, ascribe greatness to our G-d and bless His Name'. The Chachamim learn from here that the response to a B'rachah in the Beis-Hamikdash is 'Baruch Shem K'vod Malchuso le'Olam Va'ed'. 1
Rashi #2 (in B'rachos, 21a): 'When Moshe came to begin the words of the Shirah, he said to Yisrael "When I bless Hashem, you answer after me 'Amen!' When I call out the Name of Hashem in the form of a B'rachah, you answer after me 'Amen!' 2
Ramban: Refer to 32:1:3:5**.
Rashbam: 'When I relate to you the mighty deeds and kindnesses that Hashem did for you and that He is righteous becausse of what He will do for you in the future, ascribe greatness to Him and acknowledge the truth (verbally).
Seforno: 'When I Daven 3 to Hashem' - for the ingathering of the exiles 4 and for the coming of Mashi'ach, 5 you, who know Hashem's greatness via the many miracles recorded in the Torah when you hear from me in the Shirah things that will happen to Yisrael, don't attribute it to change, assuming that He has turned into your enemy, but ascribe greatness to our G-d'. 6
B'rachos, 21a: It teaches us the obligation to recite a B'rachah (Birkas ha'Torah) before learning Torah. 7
B'rachos, 45a: We learn from "Ekra" (singular) and "Havu Godel" (plural) that when three people eat together they are obligated to recite Birchas ha'Mazon with a Zimun. 8
Yerushalmi B'rachos, 7:1: We learn via a Gezeirah Shavah "Sham" "Sham" 9 from the Pasuk in Eikev "u'Veirachta es Hashem" that just as eating requires a B'rachah afterwards, so to, does learning Torah require a B'rachah afterwards.
Targum Onkelos and Targum Yonasan: 'When I recite the Name of Hashem in prayer, ascribe (honor and - Targum Yonasan) greatness to our G-d'. 10
Sifri: It teaches us that when they (presumably, this is referring to the Chazan) recite "Barchu es Hashem ha'Mevorach", the congregation should respond 'Baruch Hashem ha'Mevorch Le'olam Va'ed', and when one person recites 'Yehei Sh'meih Rabah Mevorach', the others respond 'le'Olam u'le'Olmei Olmaya'. 11
Hadar Zekenim and Rosh: 'When I praise Hashem, you - the four winds (Refer to 32:2:1:10 & 32:2:3:7), Heaven and earth, ascribe greatness to Him. You must praise him for Keri'as ha'Torah, on the merit of which you exist; 12 and just like you benefit the world, so do My teaching gives life to the world and heals it.
Teshuvos ha'Rosh: It teaches us that whenever one hears a B'rachah ('Baruch Atah Hashem'), one should respond 'Baruch Hu u'Varuch Sh'mo'. 13
See Sifsei Chachamim and Torah Temimah, note 33, who elaborates.
Moshe said this this specifically in connection with Shiras Ha'azinu. He did mention it in connection with Shiras ha'Yam ("Az Yashir"), because Yisrael sang it together with Moshe, or in connecion with the Shiras ha'Be'er ("Ali Be'er Enu lah'), because, Yisrael sang it lone and because Hashem's is not mentiooned there. See Oznayim la'Torah.
Seforno: As in Eichah, 3:55 and in Tehilim, 99:6.
Seforno: In Pasuk 11.
Seforno: In Pasuk 12, 43.
Seforno: Since you know that Hashem can save you.
'Asher Bachar banu ... '. See also Torah Temimah, note 29.
One person blesses Hashem and the other two respond. See Torah Temimah, note 32.
Presumably, this ought to read 'Hashem' 'Hashem'. See Torah Temimah, note 30.
See answer #5. Targum Yonasan: Woe to those who mention the Name of Hashem 'recklessly!' See how Moshe the Rebbe of Yisrael was not able to mention it before saying eighty-five letters and twenty-one words.
See answer #7 and note. See also Torah Temimah, note 35.
Hadar Zekenim and Rosh: As the Navi writes in Yirmiyah 33:25 "Im Lo Berisi, Yomam va'Laylah, Chukos Shamayim va'Aretz Lo Samti".
See Torah Temimah, note 36.
