"Linux is a cancer that attaches itself in an intellectual property sense to everything it touches." Steve Ballmer, Microsoft CEO 
Microsoft Corporation is global software company based out of Redmond Washington. They are pretty famous, mostly for having written Microsoft Windows, which along with Microsoft Office made them one of the wealthiest and most powerful software companies in the world. In fact, it made them powerful enough to succesfully win in a legal case against the US government who went after them after it became clear that they were breaking some basic anti-trust rules. Unfortunately, while they were found guilty (twice) there has been criticism that they have never been seriously punished.
In 2004 a similar case was brought in Europe. Microsoft was found guilty of breaking anti-trust laws, fined 497M Euros ($613M) and ordered to unbundle Windows their Windows Media Player software from Windows. Despite being a European record, the fine is around 0.1% of Bill Gates' personal fortune, and many Microsoft detractors believe forcing them to support open standards such as ogg would have done more to stop monopolising.
Though they grew to their large size because they dominated the PC desktop with Windows, they have been focusing for the last eight or more years (since the rollout of NT 4.0 in 1996) on dominating as an enterprise software solution, pushing products like Microsoft Exchange, Microsoft SQL Server, Active Directory, SMS, and a number of other enterprise products.
Most of Microsofts products have some open source competition, to which some find to be better than Redmond's equivalents, and some of which is worse.
Microsoft was put on the map back when IBM wanted to create a "personal computer" to compete with the popularity of the products from Apple Computer. IBM wanted to use CP/M as the operating system for this PC they were creating, but were turned away by CP/M's creator Digital Research in a fluke. Gates, Ballmer and Allen, not missing an opportunity, promised IBM an OS for their PC, so they bought QDOS from Tim Paterson for a mere $50,000, called it MS-DOS and the rest is history. Prior to this OS, Microsoft was mostly known for BASIC and a small handful of other programming languages.