Glasses have been used to make music since the middle ages, and GlassDuo are a couple who play the rare instrument, interpreting a wide range of classical and contemporary pieces on them. While there's no Yazoo, Human League or Gary Numan, you'll find a number of incredible and emotive renditions on their youtube channel. As someone with an aversion to glass it's a difficult thing to watch, but an incredible thing to hear! Invented 10 years later was the Glass Armonica, which would probably be just as hard to take on tour:
If you're interested in trying out the method for yourself, here is an article and project on singing glasses from Scientific American. As well as a project to follow, the article explains the history of singing glasses and the theory behind it. Just don't press too hard!
For the most extreme possible glass playing look no further than Justice Yeldman. Warning: NOT FOR THE FEINT HEARTED: