Nextcloud
Nextcloud describes itself as "the most popular self-hosted collaboration solution for tens of millions of users at thousands of organizations across the globe."
Share and collaborate on documents, send and receive email, manage your calendar and have video chats without data leaks. As fully on-premises solution, Nextcloud Hub provides the benefits of online collaboration without the compliance and security risks.
Licensing: GNU Affero General Public License (AGPL) v3.0 (server) (Source code)
Public instances
The following list is based on what I found while browsing the Internet and the hosts of other free services. Every instance is free -- both gratis and libre. Expanding storage (at cost) is possible with Disroot and woelkli. Expanded storage is also available "upon request" at GGC-Project.
- Chapril: 1 GB of storage. The available Nextcloud apps include calendars and tasks, contacts, music, and notes.
- Disroot: 2 GB of storage. The available Nextcloud apps include calendars and tasks, contacts, a kanban system, and notes. Disroot's Nextcloud apps also include cloud storage of bookmarks, a feed reader, and a group budget manager.
- GGC-Project: 512 MB of storage. The available Nextcloud apps include calendars, forms, and polls.
- Opendesktop.org: 5 GB of storage. Nextcloud apps include maps, music, and notes.
- wölkli: 2 GB of storage. The available Nextcloud apps include calendars and tasks, contacts, notes, and Nextcloud Talk. Nextcloud Talk supports audio and video calls, chat, "lobbies," and screen sharing. It also integrates with Nextcloud files.