In theory I think that different stacks (LAMP, Java, and Microsoft were the big contenders at the time) are similar enough in capabilities. There are a million pros and cons to each stack. But I strongly believe that how WELL you know your stack is MUCH more important than WHICH stack you use.
In other words, an experienced Java team will FAR outperform if they can use Java, and an experienced Windows team will FAR outperform if they can use Windows, and the skills of the team are much more significant than the variations between otherwise very very similar platforms. (See also http://www.joelonsoftware.com/items/2006/09/01.html).
So, when we started, Jeff was really good at Microsoft technology, so he was able to produce better code faster using Microsoft technology than if he had to learn Ruby or Python or whatever. And that was BY FAR the dominant decision point for us.
Also, the cost of Windows licenses is virtually insignificant. It's just a non-issue. Not just because of BizSpark (which we took advantage of), but because compiled C# code on Windows servers is so damn efficient you don't need very many servers. Our stack of ten web servers is SHOCKINGLY overprovisioned. They run at insanely low loads now.
It's not really C# that matters. Most web apps should be database bound, and the main database should be on a separate server, so language just shouldn't matter. SO is fast because Microsoft SQL server is fast. It's fast right out of the box, unlike every other big SQL server which needs tuning, though other servers may be a little bit faster if you tune them correctly, if you can't find a better use for your time. Also, SX splits itself into several separate sites (SO, SF, etc), so scaling the database gets even easier - it's just a different database!
Everyone should keep this in mind when they worry about server architecture - SO runs off 12 servers. As long as an app doesn't do anything crazy, it's going to scale very easily throughout the first few years. 1 server should be enough for almost anyone. 1 database, and a few frontend web app servers will take you to millions of views per day.
Unlike user software, most web apps get faster every year, and the stacks tend to get faster (due to better interpreters) not slower (due to silly 3D effects on the desktop).
pg loves to say that people who pay for server software are crazy. That might still be true for Google these days, but not for most people. You don't need many servers, and Windows is no longer slow.
Both Joel Spolsky and Jeff Atwood made several articles or blog posts explaining this. Obviously, they've got the licenses cheap; they're using the technology (WISC) they know best; and WS2008 is far, far better than any other previous MS server OS, due precisely to huge pressure from the linux challenger :)
Note : I'm a FSF member and free software fanatic, but I won't pretend that something that obviously works well, doesn't.
StackOverflow is done in ASP.NET MVC. They were one of the earliest adopters of ASP.NET MVC. It would make sense to go with Windows servers as Mono w/ Linux may not be up-to-date with latest C#/ASP.NET code. BTW, as they are part of BizSpark program, they would have got the server licences for cheap.
And I am genuinely curious as to why you think 12 Windows servers are pain compared to 12 Linux boxes?
The introduction on the Powershell Wikipedia article is a good overview . Powershell can also be used remotely, and various Microsoft products provide cmdlets (basically utilities) to use from the shell.
There are a few ways of dealing with IIS7:
* Remotely using IIS Manager 
* .NET-style configuration files - think httpd.conf
* Powershell cmdlets
SQL Server has Management Studio in various flavors, SqlCmd.exe or Powershell cmdlets.
The only time I log in to servers is to run installers or when laziness takes hold. These various tools work well enough that Microsoft offers Windows Server Core which only provides CLI access (and Powershell in the most recent version).
@Igor: For management I do feel it is a little bit more tricky since everything isn't just a text file. However, we use some Powershell, Group Policies, and WSUS as management tools (I talk about this in this post: http://blog.serverfault.com/post/1097492931/). Windows also has other management solutions I haven't gotten into yet. So although I am a believer in what Raymond refers to as Textuality in the Art of Unix Programming, it doesn't mean other options don't exist.