OK. Time for a bit of physics.
A water surface (and in fact any liquid surface) has an effect called surface tension. It's caused by the molecules of water to the side and underneath attracting the molecules on the surface. This causes a "skin" effect, but it's not a real skin. It's just that the surface behaves like a skin.
You can see from the diagram below that the molecules on the surface aren't "balanced" like the ones deep in the body of the liquid. It's this lack of balance that causes the tension.
Here's a photo of a paper clip "floating" on the surface of a glass of water:
That's why rain falls in droplets, and why fog is made up of minute water droplets.
(To be really scientific about it - and you don't need to know this - the surface has energy and any physical system naturally tends to its lowest energy state. So a water droplet tries to have the smallest surface area possible - and that is a sphere.)
Water molecules are also attracted to the surface of the glass. The strength of the attraction depends on the surface finish and the precise chemical composition of the glass. Altering the surface by abrasion or applying chemical will have an effect, which is what Jef was talking about.
If the attraction of the water molecules to the glass is weaker than their attraction to each other, the glass will be hydrophobic and the water will not wet the glass, but will run down in rivulets and form beads.
If the attraction of the water molecules to the glass is stronger than their attraction to each other, the glass will be hydrophilic and the water will wet the glass, and will give the curtain effect.
Here's a picture of the effect:
You'll notice that water tends to creep up the sides of a drinking glass. That's because drinking glasses are usually made of "soft" glass which is hydrophilic.
Here's a picture, but you can do this at home. It works with whiskey and vodka, I believe.
Adding vinegar reduces the surface tension of the water - that's why it wets the hydrophobic glass better.
To answer Phil, you can't change the nature of the glass, but you can apply finishes. As an example, so-called self-cleaning glass has a layer of titanium dioxide which is strongly hydrophilic.
You can find lots of information about surface tension by googling. Some of the pictures are quite good as well.
Oooooooooo - I LOVE physics.