Welcome!
I know what you mean... my PC's at home are almost completely Microsoft-free except that I do have to keep a couple of them with partitions for Windows for my work (and that's pretty much all I use them for
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In terms of games, I'm probably not the best person to comment on that, although it seems that Mandrake would be your best bet there - it has better support for native hardware OpenGL acceleration (RedHat probably can do this but I couldn't find it in the install process whereas it's definitely there in Mandrake 8.2).
For my purposes, though, I find RedHat does everything I need, and as long as you steer clear of the x.0 releases is very stable indeed. I've been using 7.3 for a few weeks now (from the 'Skipjack' beta) and it's been great - KDE 3 is a huge improvement.
I don't think you'll find any distributions (please, anyone correct me if I'm wrong!) that have the sort of out-of-the box multimedia support that you get from Windows. However, with just a little effort you can get a system that does everything you need.
I use "aviplay" for Windows-compatibility for video files. It does pretty much everything including all the DivX formats. You can also get completely multi-region DVD players. All these are fairly easy to install.
In terms of music, XMMS is just superb for MP3 playback and playlisting. I don't want to get into the whole Winamp/XMMS thing - they both have their own strengths and both do their jobs extremely well.
With a little coaxing, you can even get Musicmatch Jukebox to run on Linux, though in my experience it's a little flaky (the Linux version MusicMatch provide is not a native Linux app, but runs under WINE I think).
In terms of Office Applications, Sun have started charging for StarOffice (I don't begrudge them this of course, it's still better and cheaper than MS Office), so I now use OpenOffice - they've just released their 1.0.0 version and it's great in my opinion. Reads and writes MS-compatible files very well and includes more features (a proper vector drawing program for a start) than Office. If you need an integrated database suite you'll probably want to buy StarOffice 6 which includes the Adabas database (far better than MS Access, but not quite FoxPro as far as I can tell).
As a bonus you also get to use The Gimp - a full-featured photo editor almost (but not quite - yet) rivalling PhotoShop.
Scanners can be tricky to set up in Linux - particularly USB ones (mostly because the manufacturers blatantly ignore the fact that people want support for Linux/BSD) but "Sane" is coming along nicely and you might find your scanner (if you have one) is supported just fine.
Anyway, good luck...!