Oh no, not another one of these "Linux ruls, Windoze sucks and must die!!1!1" posts. Thank god, therefore, that I am not writing one. No, this is a long term prediction based on the two very different development methodologies employed in Windows vs Linux development.
To sum it up briefly, Linux's open source, distributed development by a group of passionate developers has a far greater longevity than Microsoft's hierarchical, closed-source development driven by money. But why does this make such a big difference? First lets look at the two groups drivers and what makes them do what they do.
Microsoft develops Windows as a closed-source proprietary and, most importantly, commercial product. Microsoft is a corporation and therefore needs to answer to share-holders, governments, anti-trust law makers, and other businesses. The biggest reason Microsoft develops Windows is to generate revenue. They employ developers to work on the project, and so monetary cost affects the skills and numbers of developers they can acquire. who are instructed as to what they should develop with Microsoft management guiding the direction and mission (in a holistic sense) of the design and development. They are under pressure to develop products with strict timelines in place and investors to satisfy.
Linux is developed by an organisation of non-profit developers. The developers who work on the project volunteer (for the most part) and so are driven not by the pay-check but by a passion for what they do. Generally speaking, people can select what they want to work on and what best fits their own skill sets. In addition, being open-source, anyone can get involved, and in fact they have their entire user-base available as potential contributors. Naturally not all can be developers but contributions can be made many ways. Linux does not need to answer to shareholders to justify its releases. Goals for a specific distributions release are decided upon communally so features get completed that the users actually want. Linux does not want to make money from sales of the operating system so there are no problems with anti-trust. Commercial backing, while helpful, is not necessary so Linux cannot go bankrupt or suffer cashflow problems (very applicable in the current uncertain economy) .
Its pretty much because of these differences that Linux distributions have an edge over their commercial counterparts. Microsoft, because of its reliance on being commercial, could go bang at any time. We don't know what goes on behind the closed doors of the Redmond giant. Who knows if Microsoft will be the next Exxon? Perhaps the money troubles at Microsoft are larger than they let on? Or it is possible that some new form of anti-monopoly legislation shoots them in the foot and makes it difficult for them to continue developing Windows the way they are. Who knows? We can't tell because everything at Microsoft is closed off to us and they rely on dollars, not contributors, to keep ticking. If Microsoft suddenly shut its doors, all those Windows users would be left high and dry because Windows is closed source. No one can pick it up and carry on.
Even if the financial world collapses totally, Linux wouldn't die. Being developed by passionate contributors they do not rely on a pay check to keep working. Even if a single Linux distribution nabbed 90% market share, anti-trust is not an issue because it is open-source and freely available, there isn't any direct income generated from sales of the distribution. And because of its open source nature, even if every single core developer for a Linux distribution left the project, the community behind can still keep developing it. Anyone can pick up the source code and continue development. Users wouldn't be shafted!
A timeline? I have no idea. Like I said, this is a long term prediction. It may take 2 years, may take 10. But eventually the time will come where Microsoft can no longer compete development-wise and the crown will start slipping, perhaps dramatically, perhaps over a slow, accretionary process of user disgust. Only time will tell.