I use Mozilla and Opera browsers and have found that numerous times per internet session, the browser will freeze and not take any input from my mouse or keyboard, then within a few seconds of that, the screen will fade -- like a dark "overlay" is superimposed over the screen (the overlay is like what happens when on some websites an ad appears and you have to opt out of it to continue).
After maybe 10 seconds, the overlay fades away and the screen is back to full brightness and I can interact with the browser again. I can't really say this has to do with the volume of internet traffic, it seems to happen all times of day.
I'm using Ubuntu 12.04LTS on a PC with 4gb of ram and an AMD AthlonII X4 640 Processor × 4. Does anyone have any idea what's going on?

I don't pay attention to hardware and stuff, but you may have a bad processor. If not, then there could be a bug or too many processes running at one time.

Bad processor -- I hope not. I got the computer a few months ago -- February, I think. Too many processes running -- I guess I should check the system monitor for that? But as far as a bug -- do you mean a virus, or a problem with my browsers (both Mozilla and Opera)? If it's a virus -- how do I find and eliminate it?

And this happens with those browsers only, not with other applications? Could it perhaps be a problem with some plugin that both browsers use (like Flash)?

Right -- the problem doesn't happen with other apps. I like the plug-in idea. Any thoughts on how to track it down -- trail & error? I just today installed the latest Ubuntu 12.04 updates.

When this happens, does the whole computer become unresponsive or can you switch to other applications during this? If so maybe Gnome System Monitor or something similar could reveal something..?

I can switch to other applications - I'm not in front of the computer now, but I don't believe I'm using the Gnome environment. I can't find the system monitor anyway.