<p>What is the largest heap you have personally used in a managed environment such as Java or .NET?  What were some of the performance issues you ran into, and did you end up getting a diminishing returns the larger the heap was? </p>

I am unsure what you mean by heap,  but if you mean memory used, I have used quite a bit, 2GB+. I have a web app that does image processing and it requires loading 2 large scan files into memory to do analysis.
There were performance issues. Windows would swap out lots of ram, and then that would create a lot of page faults. There was never any need for anymore than 2 images at a time as all requests were gainst those images (I only allowed  1 session per image set at a time)
For instance, to setup the files for initial viewing would take about 5 seconds. Doing simple analysis and zooming would be fairly fast once in memory, in the order of .1 to .5 seconds.
I still had to optimize, so I ended up preparsung the files and chopping into smaller peices and worked only with the peices that were required by the user at the time.