What languages does the character encoding UTF-8 support?

UTF-8 supports any unicode character, which pragmatically means any natural language (Coptic, Sinhala, Phonecian, Cherokee etc), as well as many non-spoken languages (Music notation, mathematical symbols, APL).

The stated objective of the Unicode consortium is to encompass all communications. The few exceptions which are not supported well (like Klingon) usually have a roman-alphabet equivalent and/or have an unofficial private unicode code page.

If you're concerned about a particular language, you're better off asking about that exact and particular one.

see http://www.unicode.org/charts/index.html which shows all the major code blocks (character sets) supported by unicode. Typically a character set corresponds to a language family, but the correspondence is not exactly one-to-one.

To quote the unicode website they are atleast 61 different languages supported. http://www.lexilogos.com/keyboard/index.htm

Ç'është Unicode?, in Albanian (36 letters)
ዩኒኮድ ምንድን ነው? in Amharic (http://www.lexilogos.com/keyboard/amharic.htm)
ما هي الشفرة الموحدة "يونِكود" ؟ in Arabic (36 letters)
Ի՞նչ է Յունիկոդը ? in Armenian(36 letters)
ইউনিকোড কী? in Bangla (32 letters)
ዩኒኮድ ውረኒ ግን? in Blin 
Какво е Unicode ? in Bulgarian (30 letters)
Što je Unicode? in Croatian (30 letters)
Co je Unicode? in Czech (48 letters)
Hvad er Unicode? in Danish(29 letters)
Wat is Unicode? in Dutch(26 letters)
𐐐𐐶𐐲𐐻 𐐮𐑆 𐐏𐐭𐑌𐐮𐐿𐐬𐐼? in English (Deseret)
𐑢𐑳𐑑 𐑦𐑟 𐑿𐑯𐑦𐑒𐑴𐑛? in English (Shavian)
Kio estas Unikodo? in Esperanto(31 letters)
Mikä on Unicode? in Finnish(29 letters)
Qu'est ce qu'Unicode? in French
რა არის უნიკოდი? in Georgian
Was ist Unicode? in German
Τι είναι το Unicode; in Greek (Monotonic)
Τί εἶναι τὸ Unicode; in Greek (Polytonic)
מה זה יוניקוד (Unicode)? in Hebrew
यूनिकोड क्या है? in Hindi
Mi az Unicode? in Hungarian
Hvað er Unicode? in Icelandic
Gịnị bụ Yunikod? in Igbo
Que es Unicode? in Interlingua
Cos'è Unicode? in Italian
ユニコードとはか？in Japanese
ಯುನಿಕೋಡ್ ಎಂದರೇನು? in Kannada
유니코드에 대해? in Korean
Kas tai yra Unikodas? in Lithuanian
Што е Unicode? in Macedonian
X'inhu l-Unicode? in Maltese
Unicode гэж юу вэ? in Mongolian
युनिकोड के हो? in Nepali
Unicode, qu'es aquò? in Occitan
يونی‌کُد چيست؟ in Persian
Czym jest Unikod? in Polish
O que é Unicode? in Portuguese
Ce este Unicode? in Romanian
Что такое Unicode? in Russian
ዩኒኮድ ምቃሩ? in Sebatbeit
Šta je Unicode? in Serbian (Latin)
Шта je Unicode? in Serbian
Kaj je Unicode? in Slovenian
¿Qué es Unicode? in Spanish
Vad är Unicode? in Swedish
யூனிக்கோடு என்றால் என்ன?, in Tamil
యూనీకోడ్ అంటే ఏమిటి?, in Telugu
Unicode คืออะไร? in Thai
ዩኒኮድ እንታይ ኢዩ? in Tigrigna
Що таке Юнікод? in Ukrainian
Što je Unicode? in Upper Sorbian
Evrensel Kod Nedir? in Turkish
ﻳﯘﻧﯩﻜﻮﺩ ﺩﯨﮕﻪﻥ ﻧﯩﻤﻪ؟ in Uyghur
Unicode dégen néme? in Uyghur (Latin)
Unicode là gì? in Vietnamese
Beth yw Unicode? in Welsh
ዩኒኮድ ወረጘ የጝ? in Xamtanga
Simplified Chinese
Traditional Chinese