Installation date
Knowing the installation date from the machine you are logged into can be a not so easy task. This page shows how to do it for several Linux distributions.
CentOS / Fedora
rpm -qi basesystem | grep Install
Be careful: if you upgraded your system from a previous version, this will give you the upgrade time and not first installation date.
ArchLinux
head -n1 /var/log/pacman.log
Generic
Some other generic ways that should work accross distributions, but require root access:
mount | grep " / " | awk '{ print $1 }' | xargs -I{} sudo dumpe2fs {} | grep created
mount | grep " / " | awk '{ print $1 }' | xargs -I{} sudo tune2fs -l {} | grep created