Are there any examples of incest in Hindu mythology?

Question

I am wondering if there are examples of incest relationships such as between Father/Daughter, Brother/Sister in Hindu mythology?

I would be thankful if you could mention the source.

Answer 1

There are two famous cases of incest or attempted incest in Hindu scripture, and in both cases the practice is unequivocally condemned:

1. Brahma and Saraswati: As I discuss in this answer, when Brahma created Saraswati, he immediately fell in love with her, and she evaded him by going in different directions, but he sprouted a head in each of the four directions until finally she went above him and he grew a fifth head pointed up toward Devaloka. This chapter of the Shatapatha Brahmana of the Yajur Veda describes what happened next:

   Pragâpati [Brahma] conceived a passion for his own daughter... 'May I pair with her!' thus (thinking) he united with her. This, assuredly, was a sin in the eyes of the gods. 'He who acts thus towards his own daughter, our sister, [commits a sin],' they thought. The gods then said to this god who rules over the beasts (Rudra), 'This one, surely, commits a sin who acts thus towards his own daughter, our sister. Pierce him!' Rudra [i.e. Shiva], taking aim, pierced him.

   So Shiva cut off Brahma's fifth head, which is why he only has four heads today.

2. Yama and Yami: As discussed in the scriptures in my answer here, Yama god of death and Yami goddess of the Yamuna river were twin children of Surya the sun god and his wife Sanjana. Yet Yamuna developed a desire to marry Yama, on the bizarre grounds that they slept together in the womb, and thus they should do likewise outside the womb. But Yama refused her advances, as described in Book 10 Hymnn 10 of the Rig Veda:

   I will not fold mine arms about thy body: they call it sin when one comes near his sister. Not me,—prepare thy pleasures with another: thy brother seeks not this from thee, O fair one.

Besides those two instances, there are various examples of cousin marriage and uncle-niece marriage, but those aren't considered incest.

Answer 2

Incest means sexual activity between closed blood relatives. It doesn't strictly limit to immediate family members like, father/mother, dauther/son. According to wikipedia article, at 3rd degree relatives, the common genes are 12.5%.
Now above is scientific meaning. According to Hinduism, the rules are bit changed. e.g. Gotra of a female changes upon marriage.

The sexual relation via marriage between 5th/6th degree cousins/relatives are generally acceptable and are not considered incest.

On main question, I can remember only 1 proven incest relationship (scientific way) which was between Arjun and Subhadra.
Arjun was biological son of Kunti and fathered by Lord Indra. Subhadra was biological daughter of Vasudev. Vasudev and Kunti were real brother-sister, hence Arjun and Subhadra were 1st cousins. With their mating they had son Abhimanyu.

I also came across another incest example between a (Yudhishtira like) righteous Brahmin and her biological granddaughter. This is found in Telugu Mahabharata during Anushasana Parva, during which Bhisma lying on bed gives some moral advises to Yudhishtira & brothers:

...Later Sudarsanaa was given in marriage to Agni. Agni and Sudarsanaa begot a son called Sudarsana. After marriage, Sudarsana begot a son called Oghavanta. Oghavanta begot a son and daughter called Ogharadha and Oghavati respectively. Oghavati attained marriageable age.
Oghavathi was given in marriage to Sudarsana, who is no other than her grand father. After marriage, Sudarsana took a vow that he will conquer death while adopting Grihastha dharma...

Afterwards, the Dharamadev tests the Sudarasana by going to his house in absence but disguised as a guest and asking to share bed with his wife. After lot of turmoil, the wife (i.e. granddaughter) agrees to sleep with the guest. When the Sudarasana returns home, he calls for his wife. But figures out the situation behind the closed doors. Sudarasana feels happy that he and his wife are able to serve the guest appropriately. With that Dharama takes his original form and says that he has conquered death and is eligible to go to higher worlds with physical body. His wife was intact and her half would flow as a river Oghavati through Kurukshetra and half would join along with him.