Apple, Amazon, etc. are selling these in numbers that rival game consoles. Based on the market's reaction, tablets are neither a fad nor unproven. They're the next major form factor, and I don't see them going away. This format is on the rise as traditional desktop hardware declines.
Desks are not going out of style, so whether the PC is dead isn't necessarily the right question. People will continue to sit at desks and use computers. Microsoft's style of a desktop OS, though, could be on its way out. The hardware will be changing. Gamers, high performance computing (science, 3d, graphic design) and corporate networks will be the only ones who really need the 'tower' style computers. People who just want to read mail, browse the web, listen to music and use office software could basically take a tablet and plug in a monitor, mouse and keyboard for desktop use. Which OS they are going to use, how much flexibility it has and what sort of interface is the big question.
The real contest will be between notebooks, tablets and mini-tablets (previously known as phones). To break it down even more, the issue is whether you have a keyboard, monitor and display ports built in.
I'd love to have a tiny slab the size of a 13" Macbook with no monitor or keyboard (so, even smaller!) that I could use as a desktop. Oh, oops... I just described a Mac Mini. Looks like someone is ahead of me here.