Mepis is good too. All the software in it is not "free"; it does include some proprietary apps, such as Java, Flash, RealPlayer and Adobe Reader. Some software in MEPIS does not respect the Debian Free Software Guidelines.
But, you can still download it at no cost. It has excellent hardware detection and is one of the easiest Linuxes (Linuxi?) to use. Echo Talon has almost talked me into downloading the brand new 6.0 version, which is still in beta (apparently, it's really good).
If you want Linux for an older computer, Zenwalk is a good one. I have it on a laptop right now that I use primarily as an Internet radio...433 mhz, 196 mb of ram. It's got a built in JBL sound system and actually sounds very good for having puny laptop speakers. Boots in under a minute and is extra stable (the thing crashed frequently with Win98, and XP barely ran on it).
Anyway, my two cents.
For all the other new Linux users (and maybe some not so new Linux users), you might want to check out TUX Magazine.
Articles are geared to new users, but I've learned a few things from it myself.