Cups made out of jelly
Jelloware cups: you drink out of them, then you eat them.
The best way to cut your waste is to not use disposable items to begin with but, you have to give these people some credit for the sheer weirdness of this idea. They make cups out of jelly. Once you are finished with the cup you can eat it or compost it.
The jelly is made using agar-agar, so vegetarians and vegans can eat it and the jelly can be flavoured to match or compliment the drinks inside.
You can see them in action on these sites.
Disposable cups are a problem: 1 million disposable cups are used by airline flights in the USA every six hours; every football ground I know of serves drinks in plastic cups; plastic cups are replacing glass at music festival and other events. So the potential market is huge. The Kickstarter site shows that they have achieved their funding goals - so well done to them.