The maximum amount of memory any single process on Windows can address
Mark Russinovich published a multipart series on windows memory resources really covers this very well. You can find it here: http://blogs.technet.com/b/markrussinovich/archive/2008/07/21/3092070.aspx
He covers the reasons why the limits are what they are, as well as tests. The code for the tests are floating around in the tubes somewhere.
If you want to know about memory resources and the problems you can see from leaking the various types, it is a good read.
But, in a nutshell, 32 bit on 32 bit OS: 2 GB, unless set to large address space aware, in which case 3 GB. 32 bit on 64 bit OS: 2 GB, unless set to large address space aware, in which case 4 GB.
64 bit process: 2 GB, unless set to large address space aware, in which case it could address up to 8 TB, unless it is hosted on an Intel Itanium-based systems which is limited to 7 TB.
Microsoft states the various limits (by flavors and types) at:http://msdn.microsoft.com/en-us/library/aa366778.aspx
You could write some kind of a loop in a console app to test this.
Maybe create a string that is exactly 1MB and loop through a concatenation process to increase it's size until you get a ... Stack Overflow error.
On each iteration WriteLine the size, or number of iterations.
EDIT
I would add, since STRING is immutable (despite technically being a reference type) to use OBJECT
Edit Two
Trisped points out that a string boxed in an Object is still immutable.
Creating an Array of bytes [1024] should do the trick.