Whenever a question like this comes up among the people that I am mentoring, I like to show them the "T-Shaped Employee" section of the Valve Employee handbook [0]:

"We value “T-shaped” people.

That is, people who are both generalists (highly skilled at a broad set of valuable things—the top of the T) and also experts (among the best in their field within a narrow discipline—the vertical leg of the T). This recipe is important for success at Valve. We often have to pass on people who are very strong generalists without expertise, or vice versa. An expert who is too narrow has difficulty collaborating. A generalist who doesn’t go deep enough in a single area ends up on the margins, not really contributing as an individual."

[0] - http://www.valvesoftware.com/company/Valve_Handbook_LowRes.p... page 46