Gemara

Ula said Havdalah without a closing Berachah.

Question (Beraisa): All Berachos begin and close with Baruch, except for Berachos (Rishonos) on food, on Mitzvos, a Berachah Samuch to (directly following) another Berachah, and the last Berachah of Kri'as Shma;

Some of these begin with Baruch but do not close with Baruch (e.g. for food), and some close with Baruch but do not begin with Baruch (such as a Berachah Samuch to another Berachah).

Ha'Tov veha'Metiv (the fourth Berachah of Birkas ha'Mazon) begins with 'Baruch' but does not end with 'Baruch'.

Answer: Havdalah is also like a Berachah on a Mitzvah;

The reason Berachos on Mitzvos need not end with 'Baruch' is because it is all praise (there is no interruption from the beginning Baruch) - Havdalah is also praise!

Berachos 40b - Beraisa - R. Meir: If one saw bread or a fig and said 'How nice is this bread (or fig), blessed is the One who created it', he was Yotzei;

R. Yosi says, anyone who deviates from Chachamim's text of blessings was not Yotzei.

Rav: Any Berachah without Shem (Hash-m's name) is invalid.

R. Yochanan: Any Berachah without Shem and Malchus (mention of Hash-m's kingship) is invalid.

A shepherd said 'Blessed is Rachmana (the Merciful One), the Maker of this bread'; Rav ruled that he was Yotzei.

Question: Birkas ha'Mazon requires three Berachos!

Answer: Rav said that he was Yotzei the first Berachah (Rashi - of Birkas ha'Mazon).

Support (for Rav - Abaye - Beraisa): (In Viduy Ma'aser one says) "Lo Avarti" -- I did not forget to bless You (when tithing); "v'Lo Shochachti" -- I did not forget to mention Your name (at the time).

The Beraisa does not mention Malchus!

Answer (for R. Yochanan): The Beraisa should say "v'Lo Shochachti" -- I did not forget to mention Your name and Malchus.

60b: When one wakes up he says 'Elokai Neshamah she'Nosata Bi...'

Rishonim

Rif (Berachos 28b): The Halachah follows R. Yochanan, who requires a Berachah to have Shem and Malchus.

Rambam (Hilchos Berachos 1:5): Ezra and his Beis Din enacted the text of all Berachos, so it is improper to change, add or detract from them. One who deviates from the text of a Berachah errs. Any Berachah without Shem and Malchus is not a Berachah unless it follows another Berachah.

Question: The Gemara says that one who deviates was not Yotzei - why does the Rambam say differently, that it is improper to do so, and he errs?

Answer (Kesef Mishneh): There are two kinds of deviation. If one says Chachamim's text but adds or detracts, or says the content of the Berachah .in different words, he does not err, but it is improper to do so. If one changes the content, e.g. blessed is the One who created this' (whereas Chachamim enacted to mention the type of food, e.g. fruit of the tree, he errs and was not Yotzei, like R. Yosi. Alternatively, R. Meir and R. Yosi argue about whether or not a Berachah without Shem and Malchus is a Berachah; all would agree that if he said 'Baruch Ata Hash-m Elokeinu Melech ha'Olam who created this', he was Yotzei. Nevertheless, since he deviates he errs. The second Pirush is better, for even one who says 'Blessed is Rachmana, the Maker of this bread' was Yotzei.

Rambam (ibid. 6): Berachos may be said in any language, as long as it is like Chachamim enacted. If one changed the text but mentioned Shem and Malchus and the concept of the Berachah, he was Yotzei.

Rosh (Berachos 6:23): Rav Hai Ga'on rules like R. Yochanan. The shepherd who said 'Blessed is Rachmana...' was Yotzei because he also mentioned Malchus; some texts explicitly ask this and give this answer.

Ma'adanei Yom Tov (100): Even though Rav ruled that the shepherd was Yotzei, if the Halachah follows R. Yochanan the Gemara should have asked that this is unlike R. Yochanan. The Rosh answers that from the Gemara's answer for Rav we understand the answer for R. Yochanan.

Rosh (ibid.): The Ri is unsure about the Halachah. Perhaps it follows Rav, for Abaye's Beraisa is like Rav, and R. Yochanan needs to alter the text. Since it is a Safek, if someone omitted Malchus he should not repeat the Berachah, for perhaps he was Yotzei and it is a Berachah l'Vatalah to repeat it.

Rebuttal (Tosfos Berachos 40b DH Amar): R. Yochanan need not alter the text of the Beraisa - the Tana is not a peddler, he need not mention every detail of the Berachah! R. Yochanan requires 'Melech ha'Olam'; saying just 'Melech' is not considered Malchus.

Question: There is no Malchus in me'Ein Sheva (Magen Avos...) (which the Shali'ach Tzibur says on Shabbos night) or in Shemoneh Esre!

Answer: R. Yosi considers "Shma Yisrael..." to be a verse of Malchus (Rosh Hashanah 32b). Similarly, 'Ha'Kel ha'Kadosh Baruch Hu' me'Ein Sheva is considered Malchus, and 'Ha'Kel ha'Gadol' in the first Berachah of Shemoneh Esre. Alternatively, 'Elokei Avraham' is considered Malchus, for Avraham made Hash-m known to the world.

Question (Kesef Mishneh ibid.): Just like a Berachah Samuch to another Berachah need not begin with Baruch, it does not need Malchus. But Elokai Neshamah is not connected to Asher Yotzar, and it does not have Malchus!

Answer #1 (Kesef Mishneh): Elokai is considered Malchus.

Answer #2 (Tosfos 104b DH Kol): This was not enacted like a Berachah. Rather, it is words of praise and supplication to Hash-m. The same applies to 'Atah Hu Ad she'Lo Nivra...' (in Korbanos after Shma) and Tefilas ha'Derech.

Rambam (ibid. 11:1): All Berachos begin and close with Baruch, except for the last Berachah of Shma, a Berachah Samuch to another Berachah, a Berachah (Rishonah) on food or similar Berachos, and Berachos on doing Mitzvos.

Question: The Sheva Berachos for Chasan and Kalah are Samuch to each other, nevertheless most begin with Baruch!

Answer #1 (Rashi Kesuvos 8a DH Same'ach): Those Berachos were enacted independently or are sometimes said by themselves.

Answer #2 (R. Tam, in Tosfos DH Chutz): Many of these Berachos are short; the opening is also the closing, just like Berachos before food. A Berachah following a short Berachah (which does not close with Baruch) must begin with Baruch, for otherwise they would appear like one long Berachah. The same applies to Havdalah. We must say that v'Ha'arev Na in Birkas ha'Torah is not a separate Berachah - if it was, it would have to begin with Baruch, since the previous Berachah is short! However, the Yerushalmi says that Havdalah begins with Baruch because it can be said without the others.

Question: The closing Berachah of Hallel, Yishtabach, and Yir'u Einenu (said in Chutz la'Aretz before Shemoneh Esre of Ma'ariv) do not begin with Baruch!

Answer #1 (Tosfos ibid.): These are Samuch to the opening Berachah of Hallel, Baruch she'Amar, and Hashkiveinu, respectively. Therefore, one must be careful not to interrupt between Baruch she'Amar and Yishtabach.

Question: We close Hallel on Seder night with Yehalelucha, even though there is no opening Berachah!

Answer #1 (and Answer #2 to Question (iv) - Tosfos ibid.): A Berachah after verses need not begin with Baruch, for it is clear where the Berachah begins.

Answer #2 (Ro'oh Berachos 46b Sof DH veha'Tov): Yehalelucha was not enacted to be Berachos. Rather, it is praise and thanks to Hash-m. The same applies to Elokai Neshamah, the short prayer for one who travels in a dangerous place (Berachos 29b, 'May Yisrael's needs be in front of You...'), and the Berachah for rain.

Rambam (ibid.) Some of these Berachos of praise begin with Baruch but do not end with Baruch, and some end with Baruch but do not begin with Baruch. Only a few Berachos for Mitzvos are exceptions (they begin and end with Baruch), such as reading in the Sefer Torah and for seeing graves of Yisrael; all the rest begin with Baruch but do not end with Baruch.

Objection (Ra'avad): There are other Birkos ha'Mitzvos of praise that begin and end with Baruch, e.g. Kidush and Havdalah! Rather, wherever Chachamim saw fit to make a long Berachah they enacted to close with a Berachah.

Kesef Mishneh: An old text of the Rambam says that the Berachos for Sefer Torah and for graves of Yisrael are examples of Berachos that begin and end with Baruch.

Rambam (Hilchos Kri'as Shma 1:7): Chachamim fixed texts for Berachos. Some begin with Baruch, others do not; some close with Baruch, others do not. One who deviates from the text of a Berachah errs, and must repeat the Berachah.

Question (Ramach, brought in Kesef Mishneh): One who said 'Blessed is Rachmana...' was Yotzei!

Note: The Rambam himself (Hilchos Berachos 1:6) says that if one changed the text but mentioned Shem and Malchus and the concept of the Berachah, he was Yotzei. Perhaps here the Rambam discusses changing whether or not the Berachah begins or ends with Baruch. If so, he must explain (like the Shulchan Aruch) that the shepherd was Yotzei the Berachah Rishonah, i.e. ha'Motzi. He cannot explain like Rashi, that he was Yotzei Birkas ha'Zan, for Chachamim enacted it to close with Baruch.

Poskim

Shulchan Aruch (OC 6:3): Elokai Neshamah does not begin with Baruch because it is a Berachah of praise, and such Berachos do not begin with Baruch, just like the Berachah for rain.

Question: The Tur favors this opinion, even though the Rosh (Teshuvos 4:1) says that it is because it is Samuch to Asher Yotzar!

Answer #1 (Bach DH Emnam): The Rosh agrees that it is a Berachah of praise; he merely says that it is Midas Chasidus to say it Samuch to Asher Yotzar!

Answer #2 (Gra DH Birkas): The Tur rules unlike the Rosh because the Gemara (Berachos 60b) says to say Elokai Neshamah (immediately) when one wakes up.

Mishnah Berurah (12): It is best to say Elokai Neshamah Samuch to Asher Yotzar to fulfill all opinions.

Shulchan Aruch (110:6): When the RaM mi'Rotenbork traveled early in the morning he would say Tefilas ha'Derech after Yehi Ratzon...to make it Samuch to the Berachah ha'Gomel Chasadim Tovim.

R. Yonah (Berachos 1a DH Ela, brought in Beis Yosef DH veha'RaM): Any Berachah that is normally Samuch to another Berachah does not begin with Baruch, even when it is not Samuch. The Berachah of Tefilas ha'Derech, i.e. Shome'a Tefilah, is normally Samuch (in Shemoneh Esre).

Machatzis ha'Shekel (60:2 DH v'Ayen): Nevertheless, it is better to say such a Berachah Samuch to another if possible.

Mishnah Berurah (28): If one travels during the day (after having said ha'Gomel Chasadim Tovim...), he should say Tefilas ha'Derech after a Berachah Acharonah on food or after Asher Yotzar. If this is not possible, he may say it by itself.

Kaf ha'Chayim (51): Some say that one who will travel after Shacharis should omit one of the Birkos ha'Shachar in order that he can say it before Tefilas ha'Derech. This is improper; Birkos ha'Shachar must be said in order, and they must be before Shemoneh Esre.