Given that Linux can be built starting with one system and morphed into another, you may not be able to tell precisely which it currently is. Some distribution provide the lsb tools if they are LSB compliant, so that might help.
Some distributions provide a file /etc/dist-release. For example, I have a file /etc/arch-release that is empty.
You might also execute:
uname -a
That might indicate the the distribution the kernel was built for, but that might be a long shot. My Arch linux kernel has no mention of Arch, but I believe my Gentoo install indicates "Gentoo Linux".
Some tools can be indicative of the distribution, such as apt-get, rpm, emerge, but you can usually install those tools on other distributions as well.