Stanford has open sourced a self-hosted, personal assistant system. Designed with privacy in mind. Speech recognition, analysis, task execution. They want to make so that it's easy and highly useful for everyone to integrate into their stuff. Can monitor things and filter for certain things. Aims for composability. Services (skills) are also open source and crowdsourced.
Jarvis is an ultra-light and multilingual voice assistant. Designed for home automation, it can run on energy efficient systems (eg Raspberry Pi). Very easy to use, it leaves you the choice of recognition engine and speech synthesis and installs them for you. It is extremely customizable, including via the addition of plugins. French and English.
FOSS AI personal assistant software. Implements actions/useful features, skills and API connectors. Can answer questions and ask for context for better answers (interesting!) Has a dedicated android app as well as a web interface. Written in Java, but nobody's perfect.