Gemara

(Beraisa - R. Meir): One must make 100 blessings every day - "Mah Hash-m Elokecha Sho'el me'Imach..."

On Shabbos and Yom Tov, R. Chiya brei d'Rav Avya would bless on fragrances and delicacies to fulfill 100 blessings.

Rishonim

Tosfos (DH Sho'el): Rashi says that we read "Mah" as if it said 'Me'ah (100). Some say that we read it like Me'ah so that the verse will have 100 letters. Some say that (without this,) "Sho'el" is written with a Vov, so the verse has 100 letters, to allude to 100 Berachos. Some explain that in At-Bash (we exchange Aleph and Tov, Beis and Shin...), "Mah" is Yud-Tzadi; its Gematriya is 100.

Rif and Rosh (Berachos 44b and 9:24): On Shabbos and Yom Tov there are not so many Berachos. He completes 100 through Peros.

Rosh (ibid.): Also, he should intend for the Berachos of those who read the Torah and the Maftir, and answer Amen, and they count in the calculation of 100 Berachos.

Rambam (Hilchos Tefilah 7:14): One is obligated to make 100 blessings in the day and night together. They are the 23 Berachos I mentioned in this chapter (see the Beis Yosef below), seven Berachos before and after Keri'as Shma in the morning and evening, Tzitzis, Tefilin, and 18 Berachos in each of three Tefilos. This is 86 in all. There are seven Berachos in a meal - Al Netilas Yadayim, ha'Motzi, three in Birkas ha'Mazon, and before and after the wine over which we say Birkas ha'Mazon. One eats a meal at night and one in the morning. This is 100 Berachos in all.

Rambam (15): Nowadays that they added 'Al ha'Minim' to Tefilah and 'ha'Tov veha'Metiv' to Birkas ha'Mazon, there are five extra Berachos. On Shabbos and Yom Tov there are only seven Berachos in each Tefilah, or on other days if he was not obligated in all these Berachos, e.g. he did not untie his belt (the Rambam holds that then he does not bless Ozer Yisrael bi'Gvurah) or use the bathrrom, he must complete 100 Berachos through Peros.

Hagahos Maimoniyos (80): Re'em says that everyone who reads the Torah says a Berachah before and after, and the Maftir says five. These count in the calculation of 100 Berachos. Therefore, those who read the Torah should bless loudly. In any case this is proper, so everyone can answer Amen. If he blesses quietly, to whom does he say 'Barchu'?!

Beis Yosef (OC 46 DH v'Chasuv): This connotes that one can count the Berachos only if he hears them and answers Amen. I say that even if people say them quietly, since the listener knows which Berachah it was and intends to be Yotzei and answers, he is Yotzei. This is like the great Beis ha'Keneses in Alexandria. They would wave flags, so people would know when to answer Amen, even though they did not hear (Sukah 51b).

Magen Avraham (46:7): Indeed, one who wants to be Yotzei a Berachah through another must hear the Berachah (124:8)!

R. Akiva Eiger (OC 284:3 DH v'Ya'aneh): In OC 213:2 we say that one can be Yotzei without answering Amen. Here is different. We cannot say that 'one who listens is like one who blessed', for the listener (some texts - could not have blessed himself, for he) did not read from the Torah!

Rambam (16): To complete the Berachos, he eats some vegetables, and blesses before and after. He eats a little fruit, and blesses before and after... He counts all the Berachos until he completes 100.

Teshuvas ha'Rosh (22:4): My Rebbeyim would interrupt the Shabbos morning meal, bless, and eat Seudah Shelishis afterwards. I follow them if the morning meal went until seven hours. If not (rather, I would eat Seudah Shelishis much later, after the stomach closed), it would be Achilah Gasah (stuffing myself). This is not increasing Berachos without need. It is done to honor Shabbos, to fulfill Seudah Shelishis.

Poskim

Shulchan Aruch (OC 46:3): One is obligated to make at least 100 blessings every day.

Tur: R. Natrunai Ga'on says that David enacted 100 Berachos every day. Every day, 100 Yisre'elim were dying. They did not know why. Through Ru'ach ha'Kodesh, they found out, and enacted that Yisrael say 100 Berachos every day. Chachamim enacted Birkos ha'Shachar to complete the 100 Berachos.

Note: Presumably, Birkos ha'Shachar were not enacted in the days of David. Before Anshei Keneses ha'Gedolah (at the beginning of Bayis Sheni) enacted to say 18 Berachos in each Tefilah, we would not say that they were enacted to complete the 100 Berachos?

Beis Yosef (DH d'Tanya): At night, one says ha'Mapil when going to sleep. In the morning, he blesses Al Netilas Yadayim, Asher Yatzar, and 15 Birkos ha'Shachar from Elokai Neshamah until ha'Gomel Chasadim Tovim, three Berachos on the ha'Torah, on Tzitzis, on Tefilin, Baruch she'Amar and Yishtabach, seven Berachos of Keri'as Shma, and 57 Berachos in three Tefilos. There are eight Berachos in each of two meals. This is 105 Berachos every day. If he fasts (omits the morning meal), he has eight less Berachos, i.e. 98. He blesses on Tzitzis and Tefilin at Minchah to complete 100.

Magen Avraham (8): This (98) is a printing mistake. It should say 97. We (Ashkenazim) make two Berachos on Tefilin, and bless 'ha'Nosen la'Ya'ef Ko'ach' and 'Yir'u Eineinu' (in Chutz la'Aretz, after Birkos Keri'as Shma at night), so we have 100 even on a fast day. If one fasts also the night before, he lacks eight. Perhaps he is Yotzei through hearing Chazaras ha'Shatz (the repetition of Shemoneh Esre).

Beis Yosef (ibid.): On Shabbos one lacks the Berachah on Tefilin, and 12 Berachos from each Tefilah, i.e. 37 in all. He adds Birkas me'Ein Sheva (after Ma'ariv), Kidush, seven in Musaf, and eight in Seudah Shelishis, i.e. another 17. This is 20 less than (105 of) a normal weekday. To complete the missing 15, the Gemara says that he blesses on fragrances and Peros to fulfill 100 blessings.

Magen Avraham (7): If Birkas me'Ein Sheva counts, also Chazaras ha'Shatz for three Tefilos should count! Perhaps Birkas me'Ein Sheva is different, for the individual did not say it (whereas he himself said Shemoneh Esre). This is difficult. He says (in Shemoneh Esre) 'Elokeinu... Retzei...', which is the essence of Birkas me'Ein Sheva!

Emes l'Yakov (on Tur v'Shulchan Aruch, 46:4): Based on this, on a fast day there are indeed 98 Berachos (see above, Magen Avraham 8), for we count answering to Aneinu in Chazaras ha'Shatz in Shacharis, since individuals do not say Aneinu.

Magen Avraham (7): The Beis Yosef counts Kidush like one Berachah. Really, it is one during the day, and another two at night, if he says Kidush on wine (i.e. not on bread)! We lack 13 Berachos on Shabbos. We complete them through Peros (290:1). The Shulchan Aruch (284:3) says that one is Yotzei through Birkos ha'Torah, i.e. if he does not have Peros. Keneses ha'Gedolah says so, from the Mabit (2 OC 117, 180). Will one say that R. Avahu, who completed the Berachos through fragrances and Peros, was in a city without Keri'as ha'Torah?!

Magen Avraham (7): Keneses ha'Gedolah says that on Yom Kipur, when we lack 32 Berachos, it is better to be Yotzei through Amen than through fragrances. In Shacharis and Minchah combined, we have 20 Berachos on Keri'as ha'Torah and 10 on the Haftorah. To complete the last two, he says 'Mekadesh Shimcha b'Rabim' and Modim d'Rabanan with Hash-m's name and Malchus 'Melech ha'Olam.' I disagree. One should not enter a Safek Berachah l'Vatalah in order to complete the 100 Berachos! I do not agree that one may bless on the Talis Katan by itself. (The Beis Yosef said so for one who fasts on Shabbos.) We may not increase (unnecessary) Berachos! Also the Shlah says not to smell fragrances (on fast days). Seder ha'Yom permits, and also YD 265:4. It says that we do not bring myrtle on Tish'ah b'Av, i.e. but it is permitted on Yom Kipur. However, one may bless more than once only if he diverted his mind in between. Our custom is to omit 'Al ha'Torah...' after the Haftorah at Minchah, so we lack a third Berachah. If Yom Kipur is on Shabbos, there is a seventh Aliyah in Shacharis and two more Berachos.

R. Akiva Eiger (DH v'Im): This shows that the Magen Avraham holds that we bless 'she'Asah Li Kol Tzarki' on Yom Kipur, even though one does not wear (normal) shoes.

Mishnah Berurah (14): On Yom Kipur, even counting Berachos of Aliyos and the Haftoros, we still lack three Berachos. One can complete them through fragrances or Asher Yatzar, if he uses the bathroom. In pressed circumstances, one intends that hearing Chazaras ha'Shatz count.

Mishnah Brurah (622:5): The Taz explains that we say Ein Keilokeinu on Shabbos to complete what we lack from 100 Berachos, but this is not needed on Yom Kipur, for there are many praises (to complete 100) in Tefilas Yom Kipur itself.

Beis Yosef (DH v'Chasuv): Shibolei ha'Leket (1, citing a Gaon) says that we compensate for the 20 lost Berachos on Shabbos through seven Aliyos in Shacharis and three in Minchah. Everyone blesses before and after; this makes 20. The Maftir (additionally blesses before and after the Haftorah) makes seven more Berachos.

Beis Yosef (ibid.): Those who say that Birkas ha'Torah is only two Berachos count in place of the missing Berachah 'Mekadesh Shemo b'Rabim' (after Keri'as Shma in Korbanos).

Birkei Yosef (5, citing Orchos Chayim 2): One who says 100 Berachos every day is guaranteed to be a Ben Olam ha'Ba. He profits 1000 gold pieces, for every Berachah is worth 10 gold pieces, like it says in Chulin 87a.

Kitzur Shulchan Aruch (6:7): Saying 100 Berachos every day protects from the 100 curses in Devarim.

Shevet ha'Levi (5:23, and Halichos Shlomo 22:25): Women need not must bless 100 Berachos every day. The Beis Yosef counted Berachos such as Tzitzis and Tefilin, which apply only to men, and the Poskim did not comment.

Yalkut Yosef (5) and Ashrei ha'Ish (1:7:1 citing ha'Gaon R. Y.S. Elyashiv Shlita): Women are obligated.

Shulchan Aruch (284:3): One must intend for the Berachos of those who read from the Torah and the Maftir and answer Amen. These count towards completing 100 Berachos, for we lack Berachos on Shabbos.

Gra (DH Tzarich): We say (Berachos 53b) that both the one who blesses and the one who answers are considered (as if they blessed, just the one who blesses is rewarded first).

Mishnah Berurah (6): Through answering Amen, it is as if he himself blessed.

Kaf ha'Chayim (17): It says about those who bless quietly "one sinner ruins much good."

Shulchan Aruch (290:1): One should have many Peros and delicacies (on Shabbos) and fragrances, in order to complete the count of 100 Berachos.

Bach (1): These are not unnecessary Berachos, since each time he benefits, and one may not benefit from the world without a Berachah.

Birkei Yosef (OC 46:6): Maharam Galanti (38) says that if the Peros have the same Berachah, he should command to bring them in front of him one after the other (so he can bless on each). Lev Shlomo proved from the Rosh that this is not considered an unnecessary Berachah. The Rosh holds that it is Midas Chasidus to avoid unnecessary Berachos, so we override this for any need. I disagree. The Shulchan Aruch (215:4) rules that an unnecessary Berachah is l'Vatalah. The Rambam says that it is a Torah Isur. Actually, causing oneself to need to make extra Berachos is different. The Rosh did so, for it was his only way to fulfill Seudah Shelishis properly. One may not bless with intent not to exempt more Peros that he will eat, for there are other ways to fulfill 100 Berachos. Likewise, one may not answer to Kaddish between the hand Tefilin and the head Tefilin (which obligates him to bless again), since hearing alone is like answering.

Yalkut Yosef (46:8): One may leave fruits at the end of a meal for after Birkas ha'Mazon in order to increase Berachos before and after them. One may cause an unnecessary Berachah for the sake of completing 100 Berachos. It is better to command that the Peros be brought after Birkas ha'Mazon. One may bless on fish before ha'Motzi, but he should eat less than a k'Zayis, to avoid a Safek about a Berachah Acharonah.

Kaf ha'Chayim (5): Even though we say that one is Yotzei through Berachos on the Torah, it is better to bless by himself.

Mishnah Berurah (1): It is good to complete the 100 Berachos also on Shabbos night.

Halichos Shlomo (22:23) and Teshuvos v'Hanhagos (4:60): If one started Shabbos early, Brachos he says before sundown do not count towards Berachos for Shabbos. Birkas ha'Mazon of Seudah Shlishis does not count for Shabbos if it is after dark. Yalkut Yosef (46:3) and Shevet ha'Levi (5:23) count it.

Yalkut Yosef (46:2,7): If one does not have Peros to eat, he can bless ha'Nosen Re'ach Tov ba'Peros, Al Etzei Besamim, and Al Isvei Besamim on Shabbos night and again during the day. If this is not enough, he relies on Birkos ha'Torah and Haftorah. One may bless on fragrances before Kidush, and again after Birkas ha'Mazon. However, if he knew that he will smell again later, some say that Birkas ha'Mazon is not a Hefsek. Therefore, he may not bless again.