Gemara

Mishnah: They bring to him Chazeres (if he has no other vegetable for Karpas). He dips (and eats) Chazeres before eating Matzah. Afterwards, they bring Matzah and Chazeres (for the Mitzvah of Maror)...

Reish Lakish: This teaches that Mitzvos require intent. The first time he ate Chazeres it was not the time for the Mitzvah of Maror, and he blessed like usual for a vegetable; perhaps he did not intend for the Mitzvah. Therefore, he must eat Maror again afterwards.

If Mitzvos did not require intent, he would not need to eat again, for he would be Yotzei the first time!

Question #1: Perhaps Mitzvos do not require intent, and he dips again to arouse the children!

Suggestion: If the Mishnah does not teach that Mitzvos require intent, it should discuss a different vegetable for Karpas!

Rejection: Had it discussed another vegetable, we would have thought that one dips twice only if he has another vegetable. Therefore the Mishnah teaches that even if he has only Chazeres, he dips twice.

Question #2 (Beraisa): If one ate Maror without intent, he was Yotzei.

Answer to both questions: Tana'im argue about this.

(Beraisa - R. Yosi): Even though he dipped (and ate) Chazeres (for Karpas), it is a Mitzvah to bring Chazeres, Charoses and two cooked foods.

Question: Perhaps R. Yosi holds that Mitzvos do not require intent; he dips again to arouse the children, like we said above!

Answer: If so, he would not call bringing Chazeres a Mitzvah.

Rav Huna: The first time he eats Chazeres he blesses Borei Peri ha'Adamah; the second time he blesses Al Achilas Maror.

Rav Chisda: He blesses Al Achilas Maror the first time.

The Halachah follows Rav Chisda.

Rosh Hashanah 28a: If one was forced (by Nochrim) to eat Matzah, he was Yotzei.

Rava: This teaches that one who blows a Shofar for a song is Yotzei (if he heard the right notes! Some texts attribute this to Rabah.)

Question: Obviously these are the same! What is Rava's Chidush?

Answer: One might have thought that he is Yotzei there because the Mitzvah is merely to eat Matzah, and he did so; but here "Zichron Teru'ah" is required, and one who does not intend for the Mitzvah is Mis'asek (which is not Yotzei (Mishnah 32b) - Rava teaches that this is not so.

Inference: Rava holds that Mitzvos do not require intent.

Question (Mishnah: If one was reading Parashas Shma in the Torah, and it was time for Kri'as Shma, he was Yotzei only if he had intent.

Inference: He was Yotzei only if he had intent to fulfill the Mitzvah; this teaches that Mitzvos require intent!

Answer: No; it means, if he had intent to read he was Yotzei.

Chulin 31a - Rav: If a Nidah immersed unwillingly she is permitted to her husband, but forbidden to eat Terumah

R. Yochanan: She is forbidden even to her husband.

Question: What is the case of a Nidah immersing against her will?

Suggestion: Rachel forcibly put Leah in a Mikveh.

Rejection: If so, Rachel's intention would suffice, and Leah would be permitted even to eat Terumah!

Mishnah: A healthy woman can permit a deaf, insane, or blind woman to eat Terumah (by checking her for Dam Nidah, and immersing her at the proper time).

Answer (Rav Papa): Rather, she fell from a bridge or entered the water to cool off and fell in all the way.

Rishonim

Rif (Rosh Hashanah 7b): One is Yotzei Shofar only if he and the blower both intended for this.

Source #1 (Milchamos Hash-m): R. Zeira requires intent for Mitzvos, and he is later than the Amora'im who do not require intent. (We cannot prove from the Gemara what Rava himself held.) In Pesachim, Reish Lakish himself clearly holds that Mitzvos require intent, and also Rav Huna, who says that one blesses Al Achilas Maror the second time he eats it.

Source #2 (Rosh, Rosh Hashanah 3:11): In Pesachim R. Yosi holds like R. Zeira, and 'Nimuko Imo' (the Halachah follows R. Yosi because he had great reasons for his opinions). The Yerushalmi learns from a Mishnah of Shofar and Megilah that Mitzvos require intent. The Bavli also sought to learn this from a Beraisa; the rebuttals given are poor, for the text of the Mishnah and Beraisa connotes otherwise.

Rebuttal (Or Zaru'a in Hagahos Ashri): R. Zeira is the only Amora who says that Mitzvos require intent. Several Amora'im and the Stam Gemara do not require intent. The Halachah follows Rav, who says that accidental immersion permits a Nidah to her husband (Chulin 31a).

Rambam (Hilchos Chametz u'Matzah 6:3): If one ate Matzah without intention, e.g. Nochrim forced him to eat, he was Yotzei.

Magid Mishnah: Some say that he was Yotzei only if he knew that it is Pesach and he is obligated to eat

Rambam (Hilchos Kri'as Shma 2:1): One is Yotzei Shma only if he had intent in the first verse.

Rambam (Hilchos Shofar 2:4): One who hears a Shofar is not Yotzei unless he and the blower both intended that he be Yotzei.

Question: Regarding Matzah, the Rambam says that one is Yotzei even without intent!

Answer #1 (Ra'avad brought in R. Mano'ach (Hilchos Chametz u'Matzah ibid.), and Ran (DH Lefichach) brought in Kesef Mishneh): The Rambam holds that Mitzvos require intent. However, we find that Mis'asek is normally exempt from a Korban, except when a person physically benefited from the transgression (it is as if he intended). Similarly, one is Yotzei without intent regarding Matzah because he physically benefited!

Pri Megadim (Petichah Klalis 3:5): It is unclear whether or not one who was forced to eat Maror was Yotzei, for it is bitter and harmful.

Answer #2 (Magid Mishnah): The Rambam holds that since one merely hears the Shofar, intent is required. Since one is Yotzei Matzah through an action, intent is not required. This is unlike Rabah, who equated these Mitzvos. The Gemara inferred that Rabah holds that Mitzvos require intent, but it did not say so about the teaching that one who was forced to eat was Yotzei.

Source (R. Yonah Berachos 6a DH Emnam): An action is in place of intent. Speech depends on the heart, so if one spoke without intent he did not do anything that can be considered a Mitzvah.

Rebuttal (Magid Mishnah): We do not find a distinction between Mitzvos regarding whether or not intent is required. Perhaps the text of the Rambam should say that he is not Yotzei Matzah.

Defense of Answer #2 (Lechem Mishneh): Perhaps this is the Gemara's answer why it is not obvious that Matzah and Shofar are the same! Presumably, the Magid Mishnah's text of the Gemara omitted the question and answer, for he says that there is no basis for his answer in the Gemara.

Answer #3 (Yom Teru'ah 28a DH Amar): Even the opinion that requires intention for immersion agrees that if someone forced a Nidah to immerse she is Tehorah (Chulin 31a), for intent of one who forces another to do a Mitzvah helps as if the latter intended.

Question: Regarding Kri'as Shma, the Rambam requires intent only in the first verse; this is like the opinion that Mitzvos do not require intent!

Answer #1 (Lechem Mishneh): Perhaps saying Kri'as Shma is considered an action, therefore intent is not required like the Magid Mishnah answered.

Objection: The Magid Mishnah would not consider speech to be an action. Also, he suggested that the Rambam requires intent for Matzah; if so, he must have another reason to distinguish Shma from Shofar and Matzah!

Answer #2 (Lechem Mishneh): The Rambam holds like the Milchamos Hash-m, who says that Rava requires intent only in the first verse because he holds that Mitzvos require intent; in Rosh Hashanah, Rava answered on behalf of the opposing opinion.

Rosh (10:25): If one ate Maror without intent, he was Yotzei.

Poskim

Shulchan Aruch (OC 60:4): Some say that Mitzvos do not require intent.

Source (Gra DH Yesh): They follow the majority who argue with R. Zeira and R. Yosi. Also, the conclusion is that accidental immersion is Metaher (Chulin 31a), and that one fulfills the Mitzvah of Tefilin without intent (Eruvin 95b).

Ran (Rosh Hashanah 7b DH Garsinan): The argument is whether or not one needs intent to be Yotzei, but all require him to know what he is doing, e.g. he is eating Matzah and it is Pesach. If not, it would have been better to teach about this than about one who was forced!

Rebuttal (R. Yerucham, brought in Beis Yosef 475 DH Kosav ha'Rambam): We must say that the one who was forced to eat Matzah did not know that it was Matzah or that it was Pesach. One who does not want to be Yotzei is not Yotzei against his will!

Beis Yosef (589, DH Lefichach): The Ro'oh learns from here that one is Yotzei against his will; this is a minority opinion, and we are not concerned for it.

Some say that Mitzvos require intent to fulfill the Mitzvah; this is the Halachah.

Source (in addition to the Rif's sources above (b:1:i and b:1:ii - Tosfos 115a DH Maskif). If Mitzvos did not need intent, there would be no need for the Gemara to say that the Halachah follows Rav Chisda. If one was Yotzei Maror the first time, blessing Al Achilas Maror the second time is a Berachah l'Vatalah!

Note: Presumably, Tosfos holds like the Rambam, who requires eating a k'Zayis for Karpas (to obligate Netilas Yadayim; see Bi'ur Halachah 573:3: DH Pachos), or at least that one may do so. However, the Shulchan Aruch (573:6) requires eating less than a k'Zayis to avoid a Safek regarding a Berachah Acharonah. (Even though Rav Huna surely requires a k'Zayis, it is possible that Rav Chisda argues.) According to this, one is not Yotzei regardless of intent, so Tosfos has no proof!

Question: Perhaps Mitzvos do not require intent, but intent not to be Yotzei helps, therefore the Gemara must Poskin like Rav Chisda!

Answer #1: It is unreasonable to Poskin like Rav Huna and require everyone to have negative intent (see Korban Nesan'el 10:70).

Answer #2 (Bi'ur Mordechai, cited in Otzar Meforshei ha'Talmud): Negative intent does not help regarding a Mitzvah to eat.

Eshel Avraham (3): It is not clear whether or not the opinion that requires intent requires it mid'Oraisa.

Bi'ur Halachah (DH v'Yesh Omrim she'Tzrichos): The Rashbam and the Acharonim (other than the Eshel Avraham) say that the opinion that requires intent requires it mid'Oraisa.

Source #1: Rosh Hashanah 28b expounds from Zichron Teru'ah that intent is required.

Source #2 (Yom Teru'ah ibid.): Abaye (Rosh Hashanah 28b) says that if Mitzvos do not require intent...one should be liable for Bal Tosif. If all agree that mid'Oraisa intent is not required, all would agree that one transgresses Bal Tosif!

Magen Avraham (3): Mitzvos mid'Rabanan do not require intent.

Question: A Beraisa requires intent to hear the Megilah!

Answer #1 (Pri Megadim, Petichah Klalis 3:5): A Mitzvah from Nevi'im is considered like mid'Oraisa.

Answer #2 (Pri Megadim, Pesichah l'Birchos ha'Shachar DH Od Ra'isi Lehazkir): Perhaps the Magen Avraham holds that it is a Safek whom the Halachah follows, therefore we are stringent regarding Mitzvos mid'Oraisa (like the Ran, Rosh Hashanah 7b DH Lefichach), but we are lenient about Mitzvos mid'Rabanan.

Mishnah Berurah (9). According to the Magen Avraham, one would not repeat any Berachah said without intent except for Birkas ha'Mazon, since all other Berachos are mid'Rabanan. However, the Gra does not distinguish mid'Oraisa from mid'Rabanan; it appears that also the Shulchan Aruch does not. The Chayei Adam says that the argument is only when it is reasonable to say that he had a different intent, e.g. he was reading the Torah or practicing to blow. However, if one did a Mitzvah the usual way, e.g. he said Shma during Shacharis or took the Lulav (at the time of Hallel), even if he did not explicitly intend for the Mitzvah, it is clear that did it to be Yotzei.

Einayim l'Mishpat (Berachos 13a:6, citing Pri Megadim): Intent is needed only for obligatory Mitzvos such as Tefilin, not for Mitzvos such as slaughter or immersion.

Yam Shel Shlomo (Chulin 2:13): The Torah requires intent to slaughter Kodshim. We infer that Chulin does not need intent to slaughter. We require some intent (e.g. to cut or throw a knife); otherwise, it is not considered a human act. However, if one intended that it should not be slaughter, it is not considered slaughter. The argument about a Nidah who immersed accidentally depends on whether or not marital relations are considered Kodshim or Chulin.

Bach (625 DH ba'Sukos): When the Torah specifies the reason for a Mitzvah, e.g. wearing Tzitzis to remember the Mitzvos, Sukah to remember Yetzi'as Miztrayim, Tefilin so that by remembering Yetzi'as Miztrayim the Torah will be fluent in our mouths, this intent is needed to properly fulfill the Mitzvah.

Kaf ha'Chayim (10,11): A Mitzvah without intent is like a body without a Neshamah. Before any Mitzvah or prayer one should say 'l'Shem Yichud...', to unite Hash-m's name and the Shechinah. One must be extremely careful not to say this without intent.

OTHER APPLICATIONS

Mishnah Berurah (271:2): Normally, one who makes Kidush at home does not intend to be Yotzei Kidush mid'Oraisa in Shemoneh Esre (even according to the opinions that one can be Yotzei) or through Kidush in the Beis ha'Keneses. Since the Halachah is that Mitzvos require intent, one should not consider Kidush at home to be mid'Rabanan. Therefore, one must be stringent if he is in doubt whether or not he was Yotzei; also, one should not be Yotzei through a child. (For mid'Oraisa laws we do not rely on the Chazakah that a child brings Simanim immediately after 12 or 13 years.)

Bi'ur Halachah (DH Miyad): On the other hand, since some say that Mitzvos do not require intent, it is possible that one was Yotzei mid'Oraisa in Shemoneh Esre, and he cannot Motzi others who did not fulfill their Chiyuv mid'Oraisa, e.g. a wife who did not pray Ma'ariv. To fulfill (virtually) all the opinions, in such a case one should specifically intend not to be Yotzei in the Beis ha'Keneses.

Mishnah Berurah (296:36): There are varying opinions whether or not Havdalah and the Berachah of Ner are obligatory upon women. Therefore, it is best for a husband to intend not to be Yotzei in the Beis ha'Keneses in order that he can make Havdalah at home for her.