Zotero's Unicode support allows you to import, store, and cite items in any language. You can change the language of both the Zotero user interface and the citations and bibliographies created by Zotero. Finally, there is an unofficial multilingual version of Zotero, which supports storage of item metadata in more than one language (transliterations and translations).
In Zotero, the interface language defaults to matching the operating system's language. To use a different language, go to the Edit menu (Windows/Linux) or Zotero menu (Mac) and select Preferences, click on the Advanced tab, and make your selection from the Language drop-down.
To keep your Zotero UI in one language, but use another language for the citations and bibliographies created by Zotero, simply select the citation language you'd like to use from the appropriate location:
You can report mistakes in Zotero's translations in the Zotero forums. If you would like to make larger contributions (like translating the Zotero client into an as of yet unsupported language), see the developer's instructions for localization.
Juris-M (formerly called Multilingual Zotero or MLZ) is an unofficial community-driven version of Zotero that adds additional support for multilingual and legal citations. Juris-M allows you to store transliterations and translations of names, titles and other fields, and create citations and bibliographies that show this information (e.g. “Soseki, Wagahai ha neko de aru [I am a cat] (1905-06)”).
Juris-M is developed by Frank Bennett, a Zotero user and active Zotero contributor. If you would like to try out Juris-M, see the project webpage.