If you work only on the web, learn about print design and production. If you work only in print, learn the basics of web design & development. Expanding your skills will up your competitive level in a market that has become overly saturated with basic talent.
One cannot express how important it is to design for the web. The web has become an instant phenomenon that is being quickly taken over by the big dogs of the media world. Methods of content consumption based on the Internet are multiplying faster than any other form of media in the past.
First there was the Amazon Kindle, and now we have the Android-based Nook eBook reader. Rumors about Apple releasing a Tablet of their own are flying around like aimless torpedoes. If you were to ask me, Apple is definitely planning something, and it'll probably be a huge hit.
To put it simply, the world is changing very quickly. If we fail to keep up to date with what's happening, our jobs will leave us for someone else. Stay open minded and read a lot of design blogs. See what people are raving about so that you can contribute in your own way. Don't forget to collect inspiration along your journey.
PS. Print is not dead. As long as creativity isn't lost, it will continue to be a dominant form of media, regardless of the changes it goes through.