The primary advantage of using Fortran these days is that there is still a considerable amount software written in it for which there is no equivalent in a more modern language. For example LAPACK was written originally in Fortran and there have been various attempts to implement equivalent functionality in C++ and Java, but they have not reached parity with the original Fortran. In some cases it may be easier to write software in Fortran to interface with the legacy software rather than developing compatibility layers.
Aside from that there are a few bonuses that Fortran offers that other languages don't (e.g. the ** expoentiation operator), but all of these are quite minor.
The main disadvantage of Fortran is that it was created before several important advances in programming languages were developed. Eventhough several modern features have been added to Fortran over the last 20 years (for example a form of object orientation), Fortran certainly shows its age. For example, Fortran doesn't do argument type checking for functions and subroutine inputs and arguments are passed by reference by default. It is difficult to find books on Fortran these days, making even harder to learn for programmers who only know modern programming languages. For these reasons, Fortran use is usually limited to maintenance of and interfacing with legacy software.
