First, read the overview.
These are some higher-level roadmap goals. Only the first few are done, but all are various stages of implementation (as of 2013-06-12).
Filesystem backups: easy initial use case. Since you can easily put files & directories and such in Perkeep with [pk put](/cmd/pk put), you can use Perkeep for your backups. Incremental backups are basically free.
Efficient remote filesystem: should be easy to do an aggressively caching remote FUSE filesystem. Read-only is trivial. Read-write shouldn't be too painful. Every modification would be snapshotted implicitly, so revision control would be the default.
Decentralized sharing system: share anything of yours with anybody or everybody (private is the default). This is already starting to work. See sharing.
Blog / photo hosting / Document Management CMS: I intend to run my personal blog and photo / gallery hosting (with permissions) off of Perkeep. I also intend to replace my “scanningcabinet” document management software and use Perkeep instead.
Decentralized social networking: a lofty but persistent goal. For example, to implement comments or tagging: One person could use claims to attach metadata to another person‘s image blob. The signing lets you verify identity. The sharing/syncing semantics of Perkeep let you easily save a copy of all your friends’ pictures.
Import/export adapters for hosted web services: Don't worry about web services shutting down or going downhill. Mirror all your data online in your private store. Create it either in Perkeep (using open tools) and export to hosted services, or create content in hosted services and continually mirror it back into your private Perkeep. Relax knowing that your data is yours, forever.