Hashbase is described as 'Hosting for the'. There are four alternatives to Hashbase, not only websites but also apps for a variety of platforms, including Linux, Mac, Windows and Self-Hosted solutions. The best alternative is IPFS, which is both free and Open Source. Other great sites and apps similar to Hashbase are Beaker browser (Free, Open Source), Hypercore Protocol (Free, Open Source) and Solid (Free, Open Source).
IPFS is a global, versioned, peer-to-peer filesystem. It combines good ideas from Git, BitTorrent, Kademlia, SFS, and the web. It is like a single bittorrent swarm, exchanging git objects. IPFS provides an interface as simple as the HTTP web, but with permanence built in.