The question is in the title. A couple of remarks, though.
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You can choose up to 5 families.
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The poll was limited to 20 items, so I had to make choices. Sorry if your favourite isn’t in there, but you can pick “other” and tell us why.
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Some language families are very firmly established while others are more controversial. I have marked the latter with “?”
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The list of languages between brackets is by no means exhaustive. It’s just meant as an indication of some of the main ones, chosen in terms of demographics, historical and cultural importance or just plain personal preference, roughly in that order.
- Afroasiatic (Arabic, Hebrew, Hausa, Amharic, Kabyle, Ancient Egyptian)
- Niger–Congo ? (Swahili, Yoruba, Fula, Shona, Sesotho, Zulu)
- Khoisan ? (Nama, ǃXóõ)
- Algonquian (Blackfoot, Cheyenne, Cree, Mohican, Mi’kmaq, Powhatan)
- Iroquoian (Cherokee, Huron, Mohawk)
- Dené–Yeniseian ? (Ket, Tlingit, Navajo, Apache)
- Siouan (Mandan, Crow, Lakota, Dakota)
- Uto-Aztecan (Shoshoni, Comanche, Hopi, Nahuatl)
- Mayan (Classic Maya, Kʼicheʼ, Yucatec, Tzeltal)
- Quechuan (Quechuan, Aymara)
- Austronesian (Malagasy, Indonesian, Javanese, Filipino, Hawaiian, Maori)
- Dravidian (Telugu, Tamil, Kannada, Malayalam)
- Indo-European (English, French, Russian, Greek, Farsi, Hindi)
- Kartvelian (Georgian, Mingrelian)
- Sino-Tibetan (Chinese, Burmese, Tibetan)
- Kra–Dai (Thai, Lao)
- Turkic (Turkish, Tatar, Kazakh, Uzbek)
- Uralic (Finnish, Estonian, Hungarian, Sami, Mari)
- Isolates (Japanese, Korean, Basque, Sumerian)
- Other