Every Linux user will have an opinion as to which distro is "best", but in the end the choice is really yours. Since you specifically asked about distros that a Windows user could most easily adapt to though, I'd recommend SuSE, Fedora, or Mandrake (probably in that order, too). Those distros don't require as much user interaction to install and configure as a distro like Slackware does, and once installed their environment should feel pretty familiar to a Windows user. As a matter of fact, those distros often take hits from serious Linux users for making things too easy and being too "Windows-like", but if you're just starting out with Linux that's probably exactly what you want. Regardless of distro, once you've learned more about how Linux works, there's nothing stopping you from bypassing the automated setup wizards, graphical configuration utilities, etc. and getting your hands dirty by learning how to compile your own drivers or "hand-hack" your system files.
Thong_Inspector mentioned Knoppix and Mepis, which brings up a point that might be of interest to you: both of those distros are what are known as "Live CD" versions. That is, while they certainly can be installed to your hard drive just like any other operating system, they can also be run entirely from the installation disk, without touching your hard drive at all. This is a great feature for people who are just getting a feel for Linux, because they can just boot from a CD and have a fully-functioning Linux operating system running while leaving their current Windows installation totally intact. I've used a live Knoppix CD on numerous systems, and have been quite impressed with it's ability to detect and configure quite a wide range of hardware devices.
Partitioning and installation:
While you can install Linux on one single partition, it's better to have at least two partitions; one for the bulk of the operating system, and one for "swap" space. The swap file or swap partition is the same as Windows' "virtual memory" or "page file", and you get slightly better performance if swap is its own partition instead of just a file on the main partition.
For security and stability reasons, many people (including myself) make multiple partitions to create separate spaces for some of the core Linux file systems.
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