Things like Freenet or ipfs where your node doesn't provide just networking but also storage.
Could be too obvious to mention here but a fediverse instance of some sort, lots of different software you can run besides the usual suspects like Mastodon or Lemmy/Kbin ranging from the more niche microblog platforms like Misskey forks (writing this on a Sharkey instance) to things like Bookwyrm for tracking your reading habits and connecting with other book lovers.
Distributed computing like distributed.net or Folding at Home.