Red Hat Linux is probably the best-known Linux distribution. Red Hat Linux is well-supported by commercial software, and tends to be easy to install and have good hardware support out of the box.
Compaq has taken over the maintenance for Red Hat for their Alpha processor - there's a link to their Alpha Red Hat page below.
Red Hat 9 is the last version of Red Hat Linux per se, and Red Hat will stop supporting it soon. Instead they offer a commercial Linux distribution, "Red Hat Enterprise Edition", and a free distribution, "The Fedora Project".