You can create your own cloud services for things like storing photos, streaming your music collection, creating your own private messaging service, publishing websites or collaborating on projects.
The options presented here are all available through managed hosting, so you can avoid most of the technical stuff.
By the way, please do research providers before using their services.
Nextcloud is a really nice all-purpose cloud service, originally designed for businesses and governments but now available to anyone.
By default it lets you store and share files online, but the real beauty of Nextcloud is in the large range of optional add-ons ⧉ which let you create your own online services in a few clicks. For example you can sync your calendars and contacts, collaborate on documents, set up your own instant messaging service, stream your music collection, compile your own interactive cookbook and many, many other things. It has good mobile apps too.
For an in depth look at what it is and how to get started, see this site’s Beginner’s Guide to Nextcloud.
Originally a blogging service, WordPress is nowadays used to create all kinds of websites, and about one in three sites worldwide use it. There are loads of themes for it and it’s extremely customisable, so it can be used for publishing pretty much anything on the internet. (And no, you don’t need to use wordpress.com!)
Mediawiki is the software that powers Wikipedia and many other wiki sites. You can use it to create your own wiki about anything you like. By the way, wikis don’t have to be publicly edited, you can set it so that only people you authorise can edit stuff.
Big Blue Button is an online video conferencing system, kind of like having your own Zoom. Originally made for education but it can be used for anything you want. It includes the standard features of modern chat services such as groups, screen sharing, whiteboards, polls etc.
Big Blue Button managed hosting is available from Cloud68.co ⧉
Discourse is a discussion forum, like classic message boards but with modern features and options. It’s very widely used by all kinds of online communities.