1. Indo-Iranian: This branch includes languages like Hindi, Urdu, Bengali, Persian, Pashto, and Sanskrit.
2. Germanic: This branch includes languages like English, German, Dutch, Swedish, Norwegian, Icelandic, and Danish.
3. Romance: This branch includes languages like Spanish, Portuguese, French, Italian, Romanian, and Catalan.
4. Slavic: This branch includes languages like Russian, Polish, Ukrainian, Czech, Slovak, Slovene, Serbian, Croatian, Bulgarian, and Macedonian.
5. Hellenic: This branch includes Greek.
6. Celtic: This branch includes languages like Irish, Welsh, Scottish Gaelic, and Breton.
7. Italic: This branch includes Latin and its descendants, such as the Romance languages.
8. Anatolian: This branch is now extinct but included languages like Hittite and Luwian.
These are some of the main branches of the Indo-European family. There are other smaller branches as well, but these are the most commonly recognized.