It doesn't hurt to know a programming language, but people need to specialize and/or choose a specialization. If you go the web design route, Photoshop/HTML/CSS would be your weapons of choice. Pawn that off to a Programmer who does PHP/MySQL/JavaScript etc, and you're golden.
Obviously no one-man-band would have his/her own programmer, but this is where outsourcing works very well.
I messed around in school with web design/programming before and I decided to specialize in programming before I began my career. It pays in dividends if you do that.
Jack of all trades. Master of none. However, doesn't mean you have to be blind to html/css etc. Just that I can't draw/design to save my life now