Here's the one I wrote for Matt, inspired by Rudy Rucker's awesome novel Spaceland:
The Hyperman exists in four spatial dimensions. When it protrudes into ours, you see it as a series of slices (imagine that you are sticking your face through a sheet of paper, being observed by a two-dimensional flat person drawn on the page) -- the tip of the nose, the bridge, the face, the head, the back of the head.Other contributors include Michael Bishop, Elizabeth Bear, Ed Greenwood, Toby Buckell, Jay Lake, Nancy Kress and Kathe Koja. SHARED WORLDS Presents... A Fantastic Bestiary (Thanks, Matt!)
The Hyperman can go from anywhere to anywhere by taking strides through four-space. If it brings a three-dimensional object, say, a book, into the fourth dimension and rotates it on the 4D axis, it comes back into three-space with all the type backwards. If it does this with a piece of cake, it comes back with all its sugars reversed, so that you can eat it without gaining weight (but you might get explosive diarrhea).
If you want to learn more about what a 4D person is like, read Rudy Rucker's Spaceland.