Hadith: It is not impure. It is one of those who roam around among you

عن كبشة بنت كعب بن مالك -وكانت تحت ابن أبي قتادة-: أن أبا قتادة دخل فسَكَبَتْ له وَضُوءًا، فجاءت هرة فشربت منه، فأصغى لها الإناء حتى شربت، قالت كبشة: فرآني أنظر إليه، فقال: أتعجبين يا ابنة أخي؟ فقلت: نعم، فقال: إن رسول الله صلى الله عليه وسلم قال: «إنها ليست بنجس، إنها من الطوافين عليكم والطوافات».
[صحيح] - [رواه أبو داود والترمذي والنسائي وأحمد والدارمي]

Kabshah bint Ka‘b ibn Mālik, who was married to the son of Abu Qatādah, reported: Abu Qatādah came in so I poured out some water for him to use for ablution. A cat came to drink from it, so he tilted the vessel for it until it drank. Kabshah continued: He saw me looking at him and said: "Do you find it strange, O daughter of my brother?" I said: 'Yes.' He said: "The Messenger of Allah (may Allah's peace and blessings be upon him) said: 'It is not impure. It is one of those who roam around among you.'"
[Authentic hadith] - [Narrated by At-Termedhy - An-Nasaa’i - Narrated by Abu Daoud - Narrated by Ahmad - Ad-Daarimi]

Explanation

The Hadīth relates that Abu Qatādah had started making ablution when a cat came in - and cats frequently enter people's homes and mix with them. He tilted the vessel for it so it could drink from the water of ablution. Kabshah, his niece, was surprised at what he did, given that the water was prepared for ablution and it must be pure and purifying. So he related to her the Hadīth in which the Prophet (may Allah's peace and blessings be upon him) said that cats are not impure and thus do not affect the purity of water, because it is an animal that always mixes with people.