I have always regarded people who like to think up new dimensions as mental gymnasts. I find it hard enough to wrap my head around space-time, simply conceiving of the existence of other dimensions gives me a headache ;-).
I came across this particular website about a book – Imagining the Tenth Dimension – by Rob Bryanton that changed my mind. The website has a really nice flash animation about how these people conceive of higher dimensions. In the preamble, the author points out that the thoery that he puts forth is not the accepted view of todays physicists. In fact there is a lot of nice discussion about the theory in the forums.
However, if you have a few minutes and you want to limber your brains a bit without stretching it too far, check this out. Who knows, you might actually like it :-)