For red wines I'm often of a mixed opinion. While I typically use a glass with a larger opening and bowl than what I would use to pour white wine, neither do I think it will compromise the wine if you don't use a glass like this. The advantage to using a glass with a larger bowl and opening is that a) you can get your nose into the bowl and really let the aromas of the wine wash over you and b) more oxygen is allowed into the glass allowing the flavors of the wine to open up, essentially like decanting the wine but on a smaller scale.

The other question I've heard is whether the material of the glass matters. This question is much easier to answer. While crystal looks great, and I'll never not recommend it, glass is by far less expensive and since neither will have any effect on the actual taste of the wine, there's really no reason to go out and spend money on crystal when some inexpensive glass goblets will do just as well.

When it comes to which glasses to drink your wine from, the best advice I can ever give is to go to your local store and invest in some inexpensive, basic wine glasses, roughly six labeled as "red wine" and six labeled as "white wine". Most places will sell these for roughly two dollars a glass, which is great since you will eventually break some of them, and there's no reason to be replacing $50 glasses just because somebody knocked one off the table.

As a side note, when it comes to whether or not to buy glasses with or without a stem, there really isn't any difference with the notable exception of it being somewhat more difficult to knock over a glass without a stem. Personally, I'm a big fan of using stemless wine glasses for outdoor parties as you don't have to worry about them getting knocked over and having broken glass in an area that's harder to clean up. Either way, neither one will affect the taste, so whichever you prefer is always going to be fine.