These are some great handouts from Glen Keane that he handed out while I was at CalArts about drawing three dimensionally. These are high-res scans of my original copies; they can be printed on 8 1/2 x 11 or 11 x 17 paper if you're so inclined.
These say it all way better than I ever could. Again, this is an easy thing to get undisciplined about and let go. Nobody ever confronts you and says "hey, you stopped drawing three dimensionally, cut it out with all the flat drawing". Like a lot of things in life, if we can get away with something, we will. People won't usually go on a diet until their pants get too tight.
I think that drawing digitally (like in Photoshop) has made this problem more prevalent. The reason I don't like drawing in Photoshop is that I have to do a rough of each pose and then keep drawing over it with a new piece of paper each time, trying different things, and then finally I place one last piece of paper over my rough and do a more finished version. My roughs are too rough for actual storyboards, but that's okay, I like the roughing out part because I can experiment and it's easier to draw three dimensionally when I know I can just be drawing rough.
But that's not as easy with Photoshop. It's hard to look through more than one or two layers at a time in Photoshop (for me). I think it's hard for everyone else too, because it looks like most people go right to the cleaned up finished drawing in Photoshop because the roughing out and drawing over stage is very hard to do. I really think the drawings I see these days are cleaner and more polished but also more stiff and definitely not as three dimensional as they should be.
Why is this important?
Well, a drawing that works three dimensionally is always more solid and will always be a stronger drawing, for one. Obviously, if you're animating in 2D it's extremely important because as you animate your character needs to feel like its sitting in real space and if you can't draw your character from every angle then you'll never be able to turn them around as they move. But as more and more people animate in 3D this is becoming a lost discipline, I fear.
You could storyboard your whole career and never actually do a fully dimensional drawing. But I think there's a subtle effect that drawing solidly can have that makes your drawings feel more compelling and real to the viewer and really helps the audience buy the conceit that a drawing is thinking, feeling and having emotions. So I think drawing three dimensionally can make storyboards work better and connect more successfully with the audience.
I'm a bit of a crazy old crank though. I hate to blame Photoshop for everything but I think it's having a negative effect on drawing in general. Also I think I saw it buying cigarettes for minors once.