One of the great creators of optical illusions is Akiyoshi Kitaoka and the following cool illusion is by his hand (he is also the creator of the awesome “rotating snakes” illusion). As you can see in the image below, the checkerboard gives a strong sensation of “bulging out the screen”. Of course, it's just a regular checkerboard. I made the picture fuzzy, so that (to me) it appears like a mysterious sphere hovering in a dark space, but that's really just being fancy. All that is needed for the illusion to work are the little dots (a script to generate this type of images can be found here).
How does this illusion work? According Michael Bach (who's website, incidentally, contains an impressive collection of optical illusions) this is unclear. Kitoaka has a book on optical illusions, which might contain the secret, but I don't have this book in my possession and, at any rate, it's Japanese. So I will venture a guess. I think it has to do with the fact that we tend to see lines in everything. If we consider, for example, the squares in the top-right part of the checkerboard, the pattern looks like (a) in the figure below. Because we tend to interpret the margin around the small white spots as lines (b) and because these perceived lines are not perfectly aligned, we perceive a slight tilt (c). By cleverly positioning the small dots differently in different quadrants of the checkerboard, the whole checkerboard appears to be bulging!