Not Reidel (I won't spend money on something I will inevitably break), but we have a set of stemless glasses from Ikea (I think). They work just fine, don't tip over like stemware, and are really neat to look at.

As for affecting the taste... I think it's basically a myth, although I can see how some glasses will affect the flow of the liquid into your mouth, thus altering taste perception.

However, considering that I rarely spend more than 20-30 bucks on a bottle of wine, I doubt that this makes much difference. Temperature and oxygenation is FAR more important.