There are quite a few good distros. I favour Debian based ones because I like Debian's package management system & it's dependency handling.
Of the Debian based ones there's:
Debian (of course), a very stable-but-slow-to-release-the-latest-&-greatest distribution. Has *HUGE* amounts of software available for it. Has been used as the based for lots of other distributions including:
Ubuntu: A simplified version of Debian with good hardware recognition released by Mark Shuttleworth's foundation. Has fewer from-the-box software options (but what's there is certainly good). They've decided to be more of a 'here's our choice of software to do xxxx tasks'. Committed to regular release dates, unlike Debian.
Kubuntu: Ubuntu but using the KDE desktop interface instead of Gnome. KDE has a lot more choices about how you set up your machine, Gnome -by design - is a lot simpler.
Knoppix: well known amongst the Linuxim for a very, very good 'live CD' distribution with excellent hardware discovery/driver loading routines during boot. Not as optimised for hard disk install but certainly workable. Knoppix has spawned lots of live CD distros.
Kanotix: Based on Knoppix but with excellent optimisation for HD installation. It's the one I use on my laptop. It's the I use now & is the only one I've used so far that could operate my laptop's Winmodem (yech!) out of the box. It has no troubles with the internal wifi card & I think it's even set up the integral bluetooth hardware.