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For what i know, there is no standard way to know for sure…
but each Distro have their own version file you can cat somewhere.
Try these:

- “$cat /etc/redhat-release” will show you information for red hat based distros.

- “$cat /etc/SuSE-release” for SUSE based distros.

- “$cat /etc/mandrake-release” for mandrake distros.

- “$cat /etc/debian_version” for debian based distros.

- “$cat /etc/UnitedLinux-release” might also return some more information.

I also found this useful tip at linuxhelp.net:
You *might* get some clues by running “uname -r” which will show you kernel version – Some ditributors will rename the kernel to make it specific to their distro (eg, RHEL kernels have RHEL in their name)

Note:  As pointed out by Ricardo “$cat /etc/debian_version” won’t return the distro itself, but the version of the distro. Sorry :/