I host a searchable database of my physical books so that family and friends can search what I've got. Also if they run the same software, I can authorize their instance to work with a primitive inter-library search feature (their library has a public key and signs their request). Fun for book clubs!
It also hosts e-books, primarily so I can load up the website in an ebook reader and download my own books, rather than worry about connecting my reader up via cable and so on.
Also when I'm out, and I find a maybe interesting book, I can check if I have it or (if the price is too high) add it to my wishlist. Similar for relatives who wish to buy me a book. I live in Asia but primarily read in English, so I do have to capitalize on opportunities to buy books when they arise.
It's open-source, I've been running it a few years, you can use it if you like. It runs on a potato, so your 5$ VPS will be able to host several other things at the same time: