What forms of gossip/backbiting are considered haram? There is this suspicious individual who my family and I know and his friend now and then relates to me this individual's supposed true nature. He claims that he is a bad person and he relates to me his experience with him and the various misdeeds that he has committed? Am I committing a sin by listening to his friend? Or should this be taken as a warning? Should I tell his friend that I don't want to hear about what he has to say about this individual next time?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Al-Nameemah means carrying tales (gossip) to spoil the relations of people which is forbidden for the Qur'an, Hadith and the consensus of Muslim scholars. Allah condemned talebearers in His Book and said: {A slanderer, going about with calumnies} [Quran 68:11]

The Prophet said: "The tale bearer shall not enter the Paradise"
al-Hafiz al-Munziri said: 'Muslim Ummah have agreed that carrying tales is forbidden.' [ al-Zawajir ]
al-Gheebah (back biting) means speaking ill of the people in their absence. The Prophet himself defined the meaning of al-Gheebah and said: "Do not mention something about your brother (in his absence) that he would hate. Somebody said, what if what I say about my brother is true? He said: If what you said about him is true then you would have backbitten him and if it is not true, then you would have slandered him." [ Muslim ]

Allah condemned backbiting in His Book. Allah says: {…….neither backbite one another. …….} [Quran 49:12]

Therefore, the prohibition of al-Gheebah is proved by the Qur'an, Hadith and the consensus of Muslim Ummah.

Therefore, a Muslim is not allowed to listen to a person who speaks ill of people or carries their tales. Doing so helps him to practice evil and assists him to play with the dignity of people. If the backbiter does not have anyone to listen to him he will not continue doing so. Allah says: {And it has already been revealed to you in the Book (this Qur'ân) that when you hear the Verses of Allah being denied and mocked at, then sit not with them, until they engage in a talk other than that; (but if you stayed with them) certainly in that case you would be like them….. } [Quran 4:140]

Finally, you should exhort this person and advise him to avoid back biting and gossiping; if he insist on doing so then keep away from meeting or mixing with him while he plays with the honor of people.

Allah knows best.