So here's something I "made" about 2 years ago. Sorry for no pictures of it solved (I haven't been able to solve it at all). So basically what it is is a 4x4x4 Rubik's Cube with custom made stickers. I cut out all of the stickers from a few vinyl sticker sheets I have. I'm not saying I invented this idea, but this is the first one I've ever seen. I must have made this back in 2009. It's basically a 2x2x4 cube that can't shape shift. In fact, it's different from normal 2x2x4 cubes because it is that. An actual cube. It can be in positions that a normal 2x2x4 can't, so it's unique. I like to call it a bandaged 2x2x4 because sometimes it can only turn like a 2x2x2, because some pieces can end up blocking certain layers from turning. I don't recommend making one if you're not an avid cuber, since it can be a waste of time and money. If you're not lazy (like me), you can actually glue the pieces together instead of relying on just the stickers to keep it bandaged. Here's a good tutorial I found showing how to make one the non-lazy way. http://www.youtube.com/watch?v=Ly0E-kUkxVA
This is also the only bandaged 2x2x4 I could find online (though I'm sure there are a few more of these out there). I'm not taking credit for the idea, since pretty much anyone could have come up with it.