This is a compilation and index of the answers given so far. This post is community wiki, it can be edited by anybody with 100+ reputation and nobody gets reputation from it. Feel free to post your own answer and add a link to it in here (or wait for me to do it). Ideally, this answer should just be a summary (with short entries while individual other answers would have the details).
Currently actively maintained systems:
- Cygwin. A POSIX layer for Microsoft Windows. Used for Windows UNC paths.
- UWIN since 1.3. Another POSIX layer for Windows. Used at least for
//host/filenetwork file sharing paths. - @OlivierDulac IBM z/OS as mentioned in the POSIX bug tracker, z/OS resolves
//pathnamerequests to MVS datasets, not to network files. Example.
Defunct systems
- @BinaryZebra Apollo Domain/OS (confirmed). Also mentioned at Official Description UNC (Universal Naming Convention) as the possible origin of
//host/pathnotations (see also, page 2-15).
According to Donn Terry, it was HP (which acquired Domain OS) that pushed for inclusion of that provision in the POSIX spec.
- @jillagre Tektronix Utek (corroborated), where
//host/pathis a path on a distributed file system. - @roaima AT&T SysV Release 3 (unverified).
//host/pathin (discontinued in SVR4) RFS Remote File Sharing system. - @Scott SEL/Gould UTX-32 (unverified). Used for
//host/path.
Applications that treat //foo/bar specially for paths
- @Prem Perforce where
//depot/A/B/C/Drefers to a path in a depot. - @WChargin Blender. In its configuration you use a
//prefix for relative paths (to the project).