<p>Does .NET come with a class capable of representing extremely large integers, such as 100 factorial?  If not, what are some good third party libraries to accomplish this?</p>

.NET has a BigInteger class, but it is internal, unfortunately. However, several places have their own. You can grab an implementation from IronPython, or the one from CodeProject, or from Visual J#. I have to say, I've not tried these myself, so I don't know which one is the best.
http://www.codeplex.com/IronPython
http://www.codeproject.com/KB/cs/biginteger.aspx
http://msdn.microsoft.com/en-us/magazine/cc163696.aspx