Well, it looks like we may finally have an answer to the question posited in this classic column. In yesterday’s New York Times, this article describes a computer model of the shower curtain problem.
Basically, the aerodynamic drag on the water droplets creates low-pressure zones in the shower, causing the curtain to pull in. This isn’t too far from Cecil’s Coanda effect hypothesis, proving again that Cecil is the world’s smartest man.
From the NY Times article:
This apparently implies that the vortexes generated are rotating parallel to the plane of the curtain, so the eye column is perpendicular to this plane. Seems to me the vortex wall rotating against the shower curtain would also create low pressure by the Bernoulli effect.
My WAG is that this effect and the Bernoulli and Coana effects all of these contribute to the curtain pulling in. How’s that for covering myself? 
I tried a web search to find more info about how Dr. Schmidt modeled this, but no luck.
What if the shower head was overhead in the center of the ceiling? Maybe we’d get a vortex ring and Bernoulli effect would still pull the curtain in.
What if the ceiling was one big shower head? No vortexes then, I would think. Bernoulli and/or Coanda would still cause the curtain effect.
Here’s how I had always thought of it:
The shower’s rushing water creates a draft in the bathroom.
The draft has no where to blow but up since that’s where the only opening in the shower is located.
The draft blows up & around the bathroom, thus blowing the shower curtain in.
If you open the curtain a little bit while you shower, it won’t blow up anymore. My guess is that the air circulates out the top of the shower and back in through the opening in the curtain. It’s worked for me!
I saw it on Scientific American’s website where I saw it with a neat little picture of the vortex.