The only Windows-based system I can think of that is really worth considering as an alternative to the Mac mini is Dell's Studio Hybrid. Not only do I think the Hybrid looks almost as good as the Mac mini, but it can also be specced nearly identically for around the same price. Moreover, the Hybrid offers a standard DVI output and HDMI connectivity!
Of course at this point the mini pulls out the "I run Mac OS" trump card and, it should be pointed out, also has a significantly more powerful graphics chip. Nonetheless, if OS X isn't your cup of tea or you want a simple-to-setup under-the-TV computer, the Hybrid is probably the better choice.
Some competition to the Mac mini also comes, oddly enough, from Apple itself. Unless you're adamant about keeping your current monitor, keyboard, mouse and such like the iMac - especially the new £1,199 24in system - is a tempting alternative and offers an even more compact and powerful solution.
However, while configuring a system with a faster CPU, a load of RAM or a higher capacity hard drive may well push the price up, none of those upgrades are needed for the kind of day-to-day computing the Mac mini is geared towards. Simply add 2GB of RAM to the base system and the resulting £539 Mac mini will be more than happy to chew through any task the average user could possibly throw at.
For general everyday computing - web browsing, sending and reading emails, perhaps the odd bit of word processing or even kicking back and watching a DVD, the Mac mini is a more than capable machine. That it just so happens to look fantastic and have an almost infeasibly small form-factor is all the better. To see and use a Mac mini is to want one, and I can't imagine any owner being disappointed with the purchase.