How can I visualize Fortran (90 or later) source code, e.g. using Graphviz?

If you have money then Understand for Fortran is worth looking at. If you don't have money but intend to work quickly then you might get by with a trial download of the software.

For a static call graph, I've never found a free tool as useful as Understand; it's hard to find any free tools let alone a useful one. I'd write one myself but the market would be tiny :-(

For a dynamic call graph investigate your compiler options. I use the Intel Fortran Compiler which can generate a mound of useful information about an executing program. The TotalView debugger can also visualise the call graph of an executing program. You should also look at gprof2dot which makes a DOT file out of a GPROF call 'graph'. This is free and OK.

And I should also add, though it's not something I've ever used, that Callgrind may be of use.

I would recommend doxygen, which automatically generates documentation from source code (and is free). Usually you add some markup to comments describing your functions and variables. However, you can just run doxygen on undocumented source files, provided you set EXTRACT_ALL to YES in the configuration file, and have it create create relationship diagrams for all your functions (i.e. this function call these functions and is called by these other functions).

You need GraphViz installed to get diagrams generated and have the HAVE_DOT option set to YES in the configuration file.

See the doxygen documentation for graphs and diagrams for more information and this example class documentation for a example of the output generated.

Edit: Of course for Fortran you should set the OPTIMIZE_FOR_FORTRAN option to YES in the configuration file.