I’ve read that you can’t have knots in four spatial dimensions. I assume this was with ‘lines’.
Can you tie a plane into a knot in four spatial dimensions?
Absolutely! Check out this artist’s rendition
That plane only exists in three dimensions though, pravnik.
Au contraire, its flight path traverses the time dimension which is just a continuation of the three spatial dimensions we percieve. …plus it has that chick with the big knockers going through the X-ray machine. 
To answer the OP: Yes. You can knot a 2-dimensional surface in a 4-dimensional space. Typically folks study knotted spheres. Here’s a link to some images.
http://www.math.uiowa.edu/~roseman/knottedSurfaces/largeSurfaceGraphics.html
One way to construct knotted spheres in 4-space: in (w,x,y,z)-space, construct a knotted arc in the (x,y,z)-hyperplane beginning at the point (0,0,0,1) and ending at the point (0,0,0,-1). Then rotate the arc around the (w,x)-plane. The resulting surface of revolution will be a knotted sphere. The type of knotted sphere you get depends on the way you knot the original arc.
You can also twist the knotted arc as it spins around, as in the second image on ubergoober’s excellent link.
Possibly ths is not precisely on-point, but I think it is still of some relevence:
In his book The Fourth Dimension physicist Rudy Rucker describes how prominent British university (I don’t recall which one), undertook an investigation in the late 19th Century to test if ghosts were, possibly, some kind of four-dimensional phenomena. A number of prominent Spiritualists were invited to a meeting one day and they were offered a reward if could get the spirits with which they were alledgedly in contact to tie a knot in a continuous loop of rope without first cutting it apart. (That is, the knot was to appear along the strang of rope; it would, obviously, be no great challenge to tie the entire loop up in a knot).
Amazingly enough, none of the Spiritualists succeeded. One of them did, however, get a wooden ring to appear around a narrow space along the support of a pedestal table, without it being obvious that he had detached the table top from the pedestal first. He didn’t get the reward.
Slipster,
Wouldn’t that be dangerous? If you rotated matter through the fourth spatial dimension wouldn’t it become anti-matter?
KABOOM!
This stunt was associated with Henry Slade, a prominent ‘spirit medium’ of the Victorian era. There was nothing spiritual or weird about it like all Slade’s stuff, it was a trick. Spoon-bending today, wooden rings on a table leg then. Just because it’s hard to see how it’s done, doesn’t mean it’s paranormal. Incidentally, this will be the theme of the lecture I’m giving at Caltech for the Skeptics Society on June 22nd, if anyone wants to come. I’ll be demonstrating all sorts of ‘psychic miracles’.