Commentators say they will continue to become increasingly popular, so this may be a relevant topic.
I believe those commentators were referring to tablets (like the iPad), not tablet PCs. Tablet PCs simply never took off, except for some niche uses.
Tablets use hardware that derives from smartphones (with ARM-based system-on-chips), so they don't need fans (and are normally silent) and they draw little power (the biggest power draw is usually for the screen). But they can't replace PCs: they are too underpowered and their OSes (iOS or Android) are too limited for that.
Tablet PCs use laptop-class hardware and run Windows like any laptop PC, but it means that their weight and power draw is more comparable to that of a small laptop... And I think they usually have a fan. A Google search did turn up a few manufacturers of rugged tablet PCs (aimed at professional uses in difficult environments) who offer fanless (and dustpoof/waterproof/shockproof) tablet PCs, using Intel Atom CPUs (since even the ultra low power versions of the Core i5s probably draw too much power for fanless use in a very confined casing).
The distinction may be blurred a bit when Windows 8 is released though, since it will be a full-blown desktop OS, but Microsoft wants it to run on low-powered tablets too (unlike Apple and Google, who adapted their smartphone OSes for tablets).
edit: About fanless tablet PCs, it looks like there are some more consumer-grade ones too, because some convertible netbooks are fanless - the Viliv S10 Blade is one example.