How to tell which flavour of Linux I am running

When you telnet, you get it all:

login as: a087
*---------------------------------------*
Host: blahost
Company: ACME
Type: PHYSICAL
Zone: INTRANET
Environment: PRODUCTION
Location: Block

In case of problems, contact
linux@acme.com

*---------------------------------------*
a087@acme.com's password:
Last login: Tue Jul 19 17:20:14 2011 from bla.acme.com
Welcome to blahost.
This system is managed by Puppet 2.6.7.

Running Red Hat Enterprise Linux Server release 5.6 (Tikanga).



also, uname -a tells you a lot:

Linux blahost 2.6.18-238.1.1.el5 #1 SMP Tue Jan 4 13:32:19 EST 2011 x86_64 x86_64 x86_64 GNU/Linux


and in case of RedHat

cat /etc/redhat-release
Red Hat Enterprise Linux Server release 5.6 (Tikanga)

otherwise just do
ls /etc/*release