This is something I've been telling students for years.
A survey of employers released in April by the Association of American Colleges and Universities found that 93 percent of the respondents reported that a capacity to think critically, communicate clearly and solve complex problems was more important than an undergraduate major.
Indeed, companies are becoming more reliant on internships. Rolls-Royce's Krok calls them "three-month interviews." Manning-Clark, of the Colorado School of Mines, says former interns used to account for about half the recruits companies wanted to hire; now, it's about 75 percent.
Read the whole thing. I would add only one more thing and that is (especially for U.S. students) to travel abroad and gain some international exposure. You don't need to live abroad for an extended period, but having traveled to another country to gain some experience with other cultures is a big plus.
Two very good books to read are The Startup of You by Reid Hoffman and Ben Casnocha, which emphasizes the importance of entrepreneurial behavior in the workplace, and The Corner Office by Adam Bryant, which discusses what drives CEOs and what they look for in employees. The latter is based on his New York Times column of the same name and does a very good job of explaining what is important and what is less relevant for getting a job and moving ahead in your career.
In the end, however, I do want to emphasize the importance of balance and recognizing that working to live makes life meaningful, not living to work.