Question: We have an Java ERP type of application. Communication between server an client is via RMI. In peak hours there can be up to 250 users logged in and about 20 of them are working at the same time. This means that about 20 threads are live at any given time in peak hours.
The server can run for hours without any problems, but all of a sudden response times get higher and higher. Response times can be in minutes.

We are running on Windows 2008 R2 with Sun's JDK 1.6.0\_16. We have been using perfmon and Process Explorer to see what is going on. The only thing that we find odd is that when server starts to work slow, the number of handles java.exe process has opened is around 3500. I'm not saying that this is the acual problem.

I'm just curious if there are some guidelines I should follow to be able to pinpoint the problem. What tools should I use? ....

Answer: 
Sounds like the garbage collection cannot keep up and starts "halt-the-world" collecting for some reason. 

Attach with jvisualvm in the JDK when starting and have a look at the collected data when the performance drops.
The problem you'r describing is quite typical but general as well. Causes can range from memory leaks, resource contention etcetera to bad GC policies and heap/PermGen-space allocation. To point out exact problems with your application, you need to profile it (I am aware of tools like Yourkit and JProfiler). If you profile your application wisely, only some application cycles would reveal the problems otherwise profiling isn't very easy itself.