If you do anything related to numerical computations (which is a pretty huge field) learning Fortran wont be a waste of time. If you are doing anything else your time might be better spent elsewhere
Can you write a parser in it? Sure, but it's going to be painful dealing with strings. Can you write a web server? Yes, but you'd have to link to a C library that exposes the kernel TCP/IP interface to Fortran. And so, on.
So, essentially it would be like using C without a libc: it's doable, but it doesn't really make sense.