River Lethe

The River Lethe, is one of the several rivers of the Underworld, and the river of forgetfulness. Even one drop can make someone begin to forget their identity. Spirits who wish to start over (re-birth) bathe in it to completely forget who their former selves are. Then the spirits may be reincarnated into another life. Lethe was also the name of the Greek spirit of forgetfulness and oblivion, with whom the river was often identified.

The branch of a poplar tree with Lethe water dripping from it is the symbol of Hypnos.

The Demigod Files
Percy, Thalia, and Nico cross it in Percy Jackson and the Sword of Hades. The Titan Iapetus is thrown in it after Percy tosses himself and Iapetus in while they are fighting each other and forgets all about who he is (Percy didn't forget because he is is the son of Poseidon and he always stays dry so it did not affect him). Later, Percy tells him he is on the good side and his name is Bob.

Percy says it's easy for him to stay dry, but this was different. As he held it up for his friends, he could feel the river resisting him, wanting to erase the memories of them. In the end, everyone got out but Percy, who was getting weak from holding the river up. The river fell down on him, but he had time for one last thought: dry.

The Last Olympian
Nico and Percy see a vision of when Hades was talking to Maria di Angelo, in which Zeus destroys Maria di Angelo along with the hotel. Hades orders Alecto to dump Nico and his sister, Bianca, in the Lethe. He also tells her to hide them in the Lotus Hotel and Casino.

Trivia

 * In The Demigod Files, Nico states that swimming in the Lethe will turn your mind into that of a newborn baby. But the only character who has been seen dipped in the Lethe, Iapetus, was still able to speak when he arrived out. It is possible he was not submerged for long enough, although it seems likely that as he was a Titan, his mind was strong enough to partially resist it.
 * In Classical Greek, the word Lethe literally means "Oblivion", "forgetfulness" or "concealment".
 * Percy Jackson has been the only being able to go through the river and still have his whole memory intact, as Percy can resist becoming wet in water.