Theoreticaly, the current standard (Fortran 03) is not available for free; the cost of developing standards is paid for partly by the sale of these documents. However, if you poke around in the J3 documents, you might find a version of the draft of the current standard, which looks an awful lot like the real thing.
The varying length string module has been implemented by Rich Townsend and has been modified very slightly to be F conformant.
Part 3 of the Fortran standard, COCO (conditional compilation) has been implemented by Dan Nagle.
A version of the Fortran 77 standard in html form is available. It is set up with hypertext links, correct fonts, etc. This version was provided by Bill Levak. The previous version prepared from the troff version by Jeff Delinck of Inland Steel is still there.
The Fortran 77 standard is available for viewing as a text file.
Bill Levak also has provided this version of Military Standard 1753.
A copy of the official Fortran 77 interpretation that answers the question "Are functions with side effects permitted in FORTRAN 77?" and the title page of the interpretation document may be read here.
The Fortran 66 standard Unzipping produces .GIF files for viewing the pages of the standard. This version is provided by Bill Levak.
The Fortran 66 standard in PDF format