I've been able to add several thousand divs without a problem. Depends on what you'll be doing afterwards, of course, and the memory on the client machine. Everyone else is right about that.
As Harpo said, 10K is probably a good ceiling. At one time, I noticed speed problems starting at about 4K divs, but hardware has improved since then.
And, as Neil N said, adding the divs via scripting is better than having a huge HTML source.
And, to answer Harpo's comment, one way to "break it up" so that JS doesn't lock the page and produce a "page is running slowly" error is to call a timer at the end of each "add a div" routine, and the timer in turn calls your "add a div" function again.
Now, MY question is: is it possible to "paint" so that you don't need to add thousands of divs? This can be done with the canvas tag with some browsers, but I don't think it's possible with VML (the excanvas project) on IE. Or is it? I think VML "paints" by adding new elements to the DOM, at which point you may as well use DIVs, unless it's a simple shape.
Is it possible to alter the source of an image via scripting? (the image in the DOM, of course -- not the original image on the server.)