I don't think you quite understand how Linux works. Linux is the core of an operating system. There are over 200 different "Linux" operating systems including Red Hat, Fedora, CentOS, SUSE, Debian, Ubuntu, Mint, Slackware, Gentoo, PCLinuxOS, and many more. So Linux itself is a whole competition- the current leader, Ubuntu, didn't even exist until 2004. It seems like Ubuntu and Ubuntu-based distributions like Mint are still going strong. Currently, Ubuntu is going for cloud penetration and social media integration which would definitely make it more accessible. I would expect this trend to continue. Intel's Moblin interface would also have an impact here- it's a graphical interface designed for Netbooks that looks really nice. Even if Ubuntu itself doesn't adopt it (Ubuntu has its own netbook interface), some distributions would start using it. As people get more comfortable with non-Windows OSes like Android and Chrome OS, I think there's a chance that ARM-based smartbooks running Linux could gain in popularity.
As far as Windows is concerned, I think we're going to see a bigger push toward interoperability. Already, they're trying to unify Zune, Windows Phone, Windows, and XBox. It looks like Microsoft has finally decided to adopt the web standards so (finally) people won't have to write special code to get web pages working in Internet Explorer. Microsoft will continue to dominate the desktop market, largely because it is entrenched, but they'll have to work to keep their business.
Apple certainly has some interesting possibilities. They're finally starting to get to the point where OS X is a viable Windows alternative for more than just graphic designers. EA is at least attempting to bring most of their games to Mac soon after release (a month for Dragon Age: Origins) and Valve recently promised to provide all of there games, as well as the Steam client for OS X. With Source, Unreal Engine, and id Tech 5 all supporting OS X, I think we'll see an increased Mac gaming scene. This means Apple is going to internally devote more resources to this sort of thing- so maybe they won't fall so far behind on the OpenGL drivers. The potential increase in popularity also means they're going to have to improve security. Right now, there are several pieces of OS X that aren't very secure. For instance, they have to implement a full-fledged ASLR instead of the half-baked version they have now.
Oracle and HP might try to capitalize on the increased interoperability to bring out better desktop versions of Solaris and HP-UX, but with such strong pushes from both Linux and Windows, I doubt they'll be very successful.