<p>I would like to stress test a win32 application by sending a lot of random keystrokes to it, and I wonder if anyone could point me to some software I could use. Ideally, I should be able to specify which keystrokes can be sent, and control rate (random min/max).</p>

Here's a pseudocode (since you didn't mention the language you're using):
Create an array that contains the alphabet from a-z, A-Z, 0-9 (depending on what keys you wish to send)
for i = 0 to NumberOfKeyStrokes
rand() % SizeOfArray
delay for rand() milliseconds (the lower the range, the faster the key strokes are)
send via an API or as a string
For more information on sending a keystrike to an application on windows, research the API FindWindow and SendMessage