Indo-Iranian:
* Indo-Aryan: Hindi, Urdu, Bengali, Marathi, Punjabi, Gujarati, Nepali, Sinhala
* Iranian: Persian, Kurdish, Pashto, Tajik, Ossetian
Romance:
* Western Romance: Spanish, Portuguese, Catalan, French, Romansh, Italian, Sardinian
* Eastern Romance: Romanian, Moldovan, Aromanian
Germanic:
* West Germanic: English, German, Dutch, Afrikaans, Yiddish
* North Germanic: Swedish, Norwegian, Danish, Icelandic, Faroese
* East Germanic: (extinct) Gothic
Slavic:
* East Slavic: Russian, Ukrainian, Belarusian
* West Slavic: Polish, Czech, Slovak
* South Slavic: Bulgarian, Serbian, Croatian, Slovene, Macedonian
Celtic:
* Insular Celtic: Irish, Scottish Gaelic, Welsh, Manx, Cornish
* Continental Celtic: (extinct) Gaulish, Galatian
Greek:
* Modern Greek: (the sole surviving member of the Ancient Greek branch)
Italic:
* Romance: (mentioned above)
* Other Italic: (extinct) Latin, Oscan, Umbrian
Balto-Slavic:
* Baltic: Lithuanian, Latvian
* Slavic: (mentioned above)
Tocharian:
* (extinct) Tocharian A and Tocharian B, spoken in ancient Central Asia
Armenian:
* Armenian: (the only surviving member of the Armenian branch)
Albanian:
* Albanian: (the only surviving member of the Albanian branch)
This is not an exhaustive list, as there are many other smaller branches and languages within the Indo-European family.
It's important to note that some languages, like English, have been heavily influenced by other language families throughout their history, making it difficult to categorize them solely as Indo-European.