How important is it for Designers to know coding?

It would definitely make you more flexible. However all of the studios that I have worked in usually do have a designer for the visual aspect, and a developer for the core coding of it. I find that the more I code, the less I know about design, and the more I design, the less I know about code. Its the whole LeftBrain Vs RightBrain.

understanding how your designs are produced (be they print, motion, web or anything else) is important. being able to understand the limitations of production makes you a better designer. having said that, i do not think you should feel it is necessary to know how to code, the same way i do not think it is necessary for a print designer to know how to run a press. it is necessary to be able to talk to the person doing the code (or running the press) in the same language.

More knowledge never hurts. I'd definitely advise getting the XHTML down well.

At the company I work for our design and web team are considered one team. We work so close with each other that it is important to understand the coding side of things to more efficiently communicate and work with the coders. You'll have a better grasp of your media's limitations and strengths and can design around them.

There are dedicated designers and coders in a lot of places. There are only 4 designers including myself and 7 coders in our team. Then again, we focus primarily on web design. There are other designers we work with for the copy and imagery for advertisements on occasion but they still screw some things up because of their limited knowledge of code and implementation.

The more you know, the better off you are. Yes, focus on design if that is what you want to do but a general knowledge of code will get you a long way. Especially if you land a job in a smaller company. I guess it also depends on where you end up. If you are laying out printed page for a magazine, for example...