Moses is a statistical machine translation system that allows you to automatically train translation models for any language pair. All you need is a collection of translated texts (parallel corpus).
The Translate Toolkit is designed by localisers for localisers. Its aim is to make localisation easier and of higher quality. The toolkit can convert between various different translation formats and makes it possible to stay in one format across all localisation tasks.
Apertium is a machine translation platform, initially aimed at related-language pairs, but recently expanded to deal with more divergent language pairs (such as English-Catalan). The platform provides a language-independent machine translation engine, tools to manage the linguistic data necessary to build a machine translation system for a given language pair, and linguistic data for 21 language pairs, with more under development.
The platform also includes cell phone applications, blog plugins, web services and several graphical user interfaces. Apertium may translate plain text, web sites or documents without loss of formatting.
Transifex is a scalable localization platform with a focus on integrating with the existing workflow of both translators and developers. It aims to make it simple for content providers to receive quality translations from big translation communities, no matter where the project is hosted.
Project Open is a general-purpose project management system with a translation module. The source license is a GPL hybrid, and the translation module is FL (“Free License”), which is “pseudo FOSS”, with extensive limits on redistribution of code.
Virtaal is a graphical translation tool. It is meant to be easy to use and powerful at the same time. Although the initial focus is on software translation (localisation or l10n), it is definitely useful for other forms of translation.