I'm very much enamored with Debian myself. It's all I'm using these days.
What is "easy" to install depends on a lot of factors. Just to get something running, regardless of details, on reasonably new hardware, I'd say that the easiest distro I have yet met is MEPIS (which is, incidentally, Debian-based). Knoppix (also Debian-based) is almost as easy to install on the hard drive, but requires you to know a command to enter at the shell in order to get it started. I'm afraid I don't recall the command.
Both MEPIS and Knoppix are LiveCD distros, which means they boot up a fully-featured Linux distro directly from the CD. For longer-term use, rather than simply as a demonstration, I recommend installing them on the hard drive -- which you can do from within the running OS after booting from CD.
"Pure" Debian, as of the Sarge/Testing version, is absurdly easy to install as a basic, no-frills installation. The older (Woody/Stable-era) version of the installer was kind of a pain in the arse. I recommend, if you want to use Debian, to install to a machine that has broadband Internet access, and to use the install-over-Internet installation CD ISO to burn a bootable install disk, rather than downloading and burning ISOs for the full-CD install. It's faster, simpler, and less potentially problematic to use the one-CD Internet installation.
If you choose to install Debian on a machine, I recommend installing a bare-bones system, with zero additional software installed (choose the option for no extra software, and using apt later, rather than options for dselect, aptitude, apt cetera). Once it's installed, use apt to install all the software you'll want to use. This requires learning how to navigate the apt command line tools for package management, but it's a very simple system and, once you've learned it, you'll probably soon find yourself wondering how you ever survived without it.
There are other options as well, of course, for distributions -- and most distributions have their uses. Something to keep in mind is that a lot of the modern "easy to install" distributions don't work on equipment that is too old, if only because the installer might not run if there isn't enough RAM in the machine. The Anaconda installer, used for Red Hat, requires something on the order of 128MB to run (last I checked), for instance. Meanwhile, the Debian installer runs on only 32MB of RAM.