Two of the most unusual effects, apart from zero-viscosity flow, are film flow and quantized vortices.  A superfluid in a beaker will form a film that crawls up the walls, over the top, and down the sides until the beaker is emptied.  Normal fluids can also be siphoned out of containers, but only if their motion is started externally!
 
 

Now imagine that a (tightly sealed!) bucket of superfluid rotates.  A vortex can form in the middle, with fluid moving around in a circle, much like a water vortex in a draining bathtub.  The amazing difference is that, at a given distance from the vortex center, only certain fluid velocities are allowed!   There is a minimum velocity, then twice that minimum, then three times the minimum, etc.  No in-between values can occur, so the vortices are said to be quantized.

  My own research is on the behavior of superfluid vortices.

For further introduction to superfluids, I recommend D.R. Tilley and J. Tilley, ``Superfluidity and Superconductivity,'' (IOP Publishing Ltd., Bristol, 1990).  Much of the book is accessible to an advanced undergraduate physics major.