Okay, so I'll answer the question.
The pitch goes down.
What? But when I blow across a beer bottle, a full bottle produces a higher pitch than an empty one...
That's where my hint of "think about what's vibrating" comes in. When you blow across the bottle, you're making the air inside the bottle vibrate. Empty bottle = larger air cavity = longer wavelength of air vibration = lower pitch. This is not what happens when you rub a wine glass. When you rub the rim, you're making the glass vibrate. Yes, the air vibrates so you hear the sound, but the source of the vibration is the glass itself, not the air. As the glass is in contact with the water, the water becomes part of the vibrating system as well.
I'm sure the exact mechanics of what happen are rather complicated, but the glass, being quite rigid will have a restoring force to deformations (read: the glass is like a really stiff spring). Any deformation of the glass is faced with an increasing restoring force. The water does two things. It dampens the sound (the full glass will be quieter), and it provides a larger mass which must be vibrated.
The dampening component will have an effect on the pitch, but I'll ignore it. 🙂
The mass component definitely does have an effect on the pitch. Seeing as how we're ignoring dampening, we have reduced the system to something physicists love to reduce everything down to: a simple harmonic oscillator (a spring and a mass... a pendulum...). The resonant frequency of a harmonic oscillator goes as:
f = a*Sqrt[k/m]
where f is the frequency, a is some proportionality constant which makes the units work nicely, k is the spring constant, and m is the mass. If you increase m, you decrease f. Thus, adding water will decrease the frequency or pitch.
I was doing dishes earlier this afternoon. This didn't make it any more fun however.
[bill nye]NOW YOU KNOW...[/bill nye]
