My .Net Winforms application creates three OpenGL rendering contexts in my main window, and then allows the user to popup other windows where each window has two more render
As Nathan Kidd correctly said, the limit is implementation-specific, and all you can do is to run some tests on common hardware.
I was bored at today's department meeting, so i tried to piece together a bit of code which creates OpenGL contexts and tries some rendering. I tried rendering with and without textures, with and without forward-compatible OpenGL context.
It turned out that the limit is pretty high for GeForce cards (maybe even no limit). For desktop Quadro, there was limit of 128 contexts that were able to repaint correctly, the program was able to create 128 more contexts with no errors, but the windows contained rubbish.
It was even more interesting on ATi Radeon 6950, there the redrawing stopped at window #105, and creating rendering context #200 failed.
If you want to try for yourself, the program can be found here: Max OpenGL Contexts test (there is full source code + win32 binaries).
That's the result. One piece of advice - avoid using multiple contexts where possible. Multiple contexts can be understood in application running at mulitple monitors, but applications on a single monitor should resort to a single context. Context switching is slow. And that's not all. Applications where OpenGL windows are overlapped by another windows require hardware clipping regions. There is one hardware clipping region on GeForce, eight or more on Quadro (CAD applications often use windows and menus that overlap OpenGL window, in contrast with games). In case more regions are needed, rendering falls back to software - so again - having lots of OpenGL windows (contexts) is not a very good idea.