Gemara

(Rav): If a Nidah was immersed unwillingly, she is permitted to her husband, but forbidden to eat Terumah;

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

Question (Rava): Rav permits her to her husband, even though Bi'ah with a Nidah is Chayavei Kerisus. All the more so he should permit her to eat Terumah, for which there is only Misah b'Yedei Shamayim (for eating it b'Tum'ah)!

Answer (Rav Nachman): Her husband is Chulin. Tevilah for Chulin does not require intent.

Question: What is the source that Chulin does not require intent?

Answer #1 (Mishnah): If a wave containing 40 Sa'im of water separated from the sea and fell on a person and on Kelim, they are Tehorim.

Rejection: The case is, he was waiting for such a wave to fall on him;

Answer #2 (Mishnah): If Reuven's hands were Tamei and his produce fell into an irrigation channel, and he stuck his hands in and took it out, his hands become Tehorim.

Question (Rava - Beraisa): If one immersed without intent, it is as if he did not immerse.

Answer (Rav Nachman): It is as if he did not immerse for Ma'aser, but he became Tahor for Chulin.

Support (and question against R. Yochanan - Beraisa): If one immersed without intent, he is Tahor for Chulin, but not for Ma'aser.

Answer (Rav Yosef): R. Yochanan holds like another Tana:

(Beraisa - R. Yonason ben Yosef): "The garment will be washed a second time" equates the second Tevilah to the first. Just like the first Tevilah requires intent ("v'Tzivah ha'Kohen v'Chivso"), also the second.

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

Suggestion: Rachel forcibly immersed Leah.

Rejection: If so, Rachel's intention would suffice. Leah may even eat Terumah!

i. (Mishnah): A healthy woman can permit a deaf or insane woman to eat Terumah. (She checks her for Dam Nidah, and immerses her at the proper time.)

Answer (Rav Papa): According to R. Noson (who does not require any intent for Shechitah), she fell from a bridge. According to Chachamim (who require for Shechitah intent to cut), she entered the water to cool off, and fell in all the way.

Rishonim

Rambam (Hilchos Mikva'os 1:8): Anyone who immerses must intend for Tevilah. If he did not, the Tevilah helps for Chulin. Even a Nidah who immersed without intent, e.g. she fell into the water or she entered to cool off, is permitted to her husband.

Ran (Chulin 7a DH v'Hachi): The Rambam rules like Rav against R. Yochanan. This is reasonable, for Rav Nachman holds like him. Also, R. Yochanan's opinion is not even brought in Chagigah.

Rashba (31b DH ul'Inyan): We always rule like R. Yochanan against Rav. It seems that Rabah (our texts - Rava) holds like him, since he challenged Rav Nachman. Even though Rav Nachman answered, we have R. Yochanan against Rav, and Rabah against Rav Nachman, so the Halachah follows R. Yochanan. Also, we must follow the stringent opinion for Torah laws. R. Yochanan forbids mid'Oraisa, for Rav Yosef said that R. Yochanan holds like R. Yonason, and R. Yonason's law is mid'Oraisa. Even though we hold like R. Noson, who does not require intent for Shechitas Chulin, even R. Yonason admits to this. We expounded that Mis'asek (one who did not intend for the action he did) is Pasul in Kodshim (Menachos 100a). We infer that it is Kosher for Chulin. However, the Rambam rules like Rav. Perhaps he holds that the Stam Gemara, and not Rav Nachman, brought the Mishnah of a wave to show that intent is not needed for Chulin. I.e. this is the Gemara's conclusion. Even though the Gemara rejected this (perhaps he was waiting for the wave), this is a mere Dichuy (rejection), and we do not rely on it.

Hagahos Ashri (Chulin 2:8): If a Nidah immersed accidentally, e.g. she fell off a bridge or entered the river to cool off, Rav permits her to her husband. R. Yochanan forbids, even though normally Chulin does not require intent. The Halachah follows R. Yochanan against Rav. However, if Rachel forcibly immersed Leah, Rachel's intent suffices.

Poskim

Shulchan Aruch (YD 198:48): If a Nidah immersed without intent, e.g. she fell into the water or she entered to cool off, she is permitted to her husband.

i. Beis Yosef (DH Kasav): Regarding Shechitah, the Halachah follows R. Noson. Therefore, the Rambam permits her to her husband even if she fell into the water, and all the more so if she entered to cool off. He did not need to teach the latter case. Also Semag rules like Rav, and says that R. Chananel agrees. Hagahos Ashri rules like R. Yochanan. The Roke'ach says that in the Yerushalmi, R. Chanina holds like R. Yochanan, so they are a majority against Rav. R. Yerucham says that the primary opinion rules like R. Yochanan.

Bedek ha'Bayis: L'Halachah, we rule like the Rambam and those with him.

Pischei Teshuvah (26): Chamudei Daniel says that if her husband was sick, and she immersed merely to permit touching him without intent for Bi'ah, the Tevilah permits even Bi'ah.

Rema: Some are stringent and obligate her to immerse again. One should be stringent.

Bach (36 DH ha'Beis): Even R. Yochanan agrees that if Rachel forcibly immersed Leah, Rachel's intent suffices. Even if she fell off a bridge, she should not bless when she immerses again. I wrote similarly (Siman 120) regarding Tevilas Kelim.

Bach (YD Sof Siman 120 DH ha'Koneh): If one bought new Kelim from a Nochri and they fell into water, Rashi and the Ri say that he need not immerse them again. R. Menachem (Teshuvah 275) says that if one washed his hands without intent, and without diverting his mind, he decided to eat, he need not wash again. This is like Rav. Since we hold like most Poskim, who rule like R. Yochanan, he must wash again. Likewise, one should immerse the Kelim again without a Berachah. The Shulchan Aruch (120:15) rules like the Rashba, that if one immersed Kelim through a Nochri, it was valid. This is primary because he holds like Rav. We should require another Tevilah.

Bach (201 DH u'Mah she'Chasav Hilkach): The Rema is stringent for the opinion that Tevilah requires intent. If so, a wave that fell on a person is Metaher only if he was waiting for it to fall on him. The Rosh (Sof Nidah) said that the Mishnah is like R. Yosi, who say that all seas are Metaher b'Zochlin (even if the water is not collected). The Beis Yosef asked that if so, this is a Chidush even if he was waiting for the wave. What forced the Gemara to say that one might have thought to decree? I answer that had the Tana merely wanted to teach like R. Yosi, he would have taught the law directly, and not regarding a wave.

Yom Teru'ah (Rosh Hashanah 29a DH Amar): Poskim argue about whether Mitzvos require intent. The Mechaber (OC 60:4, regarding Keri'as Shma) rules like they require intent. However, he also rules (489:4) that if one asked Ploni what day of the Omer it is, and he answered, he may not count afterwards with a Berachah. He did not intend for the Mitzvah. Why was he Yotzei?! Also, if a Nidah immersed without intent, the Mechaber permits her to her husband! In OC 158:7, he says that if one washed his hands to eat a food dipped in a liquid, and afterwards he wants to eat bread, some say (that the first washing does not count, and all the more so if he washed without intent to eat). In 159:13, he says that l'Chatchilah, one should wash for bread with intent to permit eating. This connotes that Chulin requires intent l'Chatchilah. If so, he should require a Nidah to immerse again! The Rema (159:13) says that intent of the one who pours the water, or of the one whose hands are washed, suffices. Why for Shofar do we require intent of the blower and of the listener? There are many answers and Chidushim to answer these questions.

Radvaz (1:34): Most Poskim rule like R. Yochanan, for the Halachah follows him against Rav, and we follow the stringent opinion for Torah laws, especially since there is Kares for Nidah. If Rachel forcibly immersed Leah, Rachel's intent suffices. If Leah knew, she intends, just it was against her will. And even if she did not know that Rachel forces her to immerse, rather, she thinks that she just wants to throw her into water, Rachel intent suffices. The Gemara connotes like this. We should not widen the argument. However, the Rambam rules like Rav. This is reasonable. The Stam Gemara brought a proof for him. The Dichuy was weak; the Mishnah connotes that the wave is Metaher in every case, even if he was not waiting for it. The Stam Mishnah of one who put his hands into the water to retrieve his Peros proves that we do not require intent for Chulin. Even though one could say that Tevilah is more stringent than Netilas Yadayim, it seems that this is not so. Rava found a support for Rav, and we needed to establish R. Yochanan like R. Yonason. We do not require intent for Shechitas Chulin. It is mid'Oraisa, just like Nidah. Even though Shechitas Chulin pertains only to a Lav, we should not be more lenient about it. This argument does not pertain to whether Mitzvos require intent. Tevilah and Shechitah are not Mitzvos. They are Machshirin (they permit other things). Rav and R. Yochanan argue about whether Machshirin are more or less lenient than Mitzvos. The Ramban says so. It seems that the Rashba sides with the Rambam. He did not question the Rambam at all. Also the Ra'avad did not disagree. The Ri says that if one bought new Kelim (from a Nochri) and they fell into water, the Tevilah was valid. This is obvious! Even R. Yochanan agrees. Since Tevilah of new Kelim is not mid'Oraisa, it does not require intent. It is a mere Asmachta to learn from Klei Midyan. The Rambam (Hilchos Ma'achalos Asuros 17:5) says so.

Note: The Rashba says that the Rambam holds that it is a Torah law; the Ran disagrees (Kesef Mishneh 17:5).

Magen Avraham (OC 159:13): If one washed without intent to eat, and did not divert his mind, the first Netilah does not count, for it was not l'Shem Kedushah. The Rema says to wash again without a Berachah, for one opinion says that intent is not needed, so the first Netilah counted.

Pischei Teshuvah (28): Chamudei Daniel says that if Rachel forcibly immersed Leah, Rachel's intent suffices, but not if a man forced her. Levushei Serad (90) was unsure about a woman who entered the water to cool off, and afterwards intended for Tevilah, but did not lift her feet at the time of Tevilah. Perhaps she does not need another Tevilah; one can be lenient.