4D "can" be visualized in 3D: http://en.wikipedia.org/wiki/Tesseract
A "funny" note on those pictures (wich I feel is often forgotten/omitted) is that it isn't just a 3D projection, but a 2D projection of a 3D projection of a 4D object
Might sound irrelevant, but I found that this realisation made me understand the 4D objects better. you have the same kind of information loss from 3D to 2D as you do in 4D to 3D, so in the same way an animation shows 3D objects better in 2D, you "see" the 4D objects better if you rotate it. (as is shown in the animated pictures)