Although we do provide binaries for most common operating systems (Windows, MacOS, Linux), the easiest way to give gfortran a try might be to install a gfortran package provided by your OS vendor.
Debian
GFortran is included in Debian (since Etch) in the gfortran package. Old stable (lenny) contains 4.3, Stable (squeeze) contains GCC 4.4; Testing (wheezy) GCC 4.7. Depending on the Debian version, also the packages gfortran-4.1 to gfortran-4.8 are available.
Ubuntu
GFortran is inclued in Ubuntu (since Drapper) in the gfortran package. The long-term-support (LTS) version "Lucid" has GCC 4.4; Maverick has 4.4, Natty 4.5, Oneiric and Precise Pangolin (LTS) have 4.6. Quantal Quetzal has and Raring Ringtail will have 4.7.
Additionally, minor updates and new testing versions are available (installation hints).
Fedora
Fedora 19 will ship GCC/gfortran 4.9. Fedora 17 and 18 ship with GCC/gfortran 4.7. Fedora 16 and Fedora 15 ship with 4.6, Fedora 14 has 4.5, Fedora 13 has 4.4.3, Fedora 12 comes with GCC 4.4.2, Fedora 11 with GCC 4.4, Fedora 10 with 4.3.2, Fedora 9 with GCC 4.3.0; Fedora 5 to 8 come with GCC 4.1 as system compiler. Fedora 3 and 4 come with GCC 4.0.x (avoid, use at least 4.1.x)
Red Hat Enterprise Linux / CentOS
RHEL/CentOS 5.x come with GCC 4.1; newer 5.x ship also GCC 4.3 or GCC 4.4 as technical preview. RHEL/CentOS 6 has GCC 4.4. The Red Hat Developer Toolset allows to install newer GCC versions in parallel.
Mandriva
Contains gfortran in the gcc-gfortran package.
(open)SUSE
openSUSE 10.2 and SUSE Linux Enterprise (Server/Desktop) 10 contain GCC 4.1.1 (Package gcc-fortran). openSUSE 10.3 contains GCC 4.2.2 (as system compiler). openSUSE 11.0, openSUSE 11.1 and SUSE Linux Enterprise 11 feature GCC 4.3, and openSUSE 11.2 has GCC 4.4.1. openSUSE 11.3 and 11.4 use GCC 4.5.x, SUSE Linux Enterprise 11 SP1 has an optional GCC 4.5.0 on its SDK, SP2 has optionally GCC 4.6. openSUSE 12.1 ships with GCC 4.6, openSUSE 12.2 with GCC 4.7, and openSUSE 12.3 with GCC 4.7.
Builds of various GCC version (often including the experimental ones) for various openSUSE/SLE distributions can also be found on the openSUSE build service.