Comment Yes, to an extent (Score 4, Insightful) 167
The answer depends on where you want your career to go. But, regardless I would say that all programmers should invest the time to understand the business they work for so that they can best serve the interests of their employer. This is different from getting an MBA or studying business in the general sense. Programmers need to understand the problems that their company deals with, otherwise they're not going to see the best solutions.
As an example I currently work for a company that manufactures packaged food products. As the lead developer it is part of my job to understand how the business operates; from how our inventory is managed, to how our customers pay us, to how our shipping personnel process incoming and outgoing items. Understanding this and talking to people in all these areas allows me to spot inefficiencies and address problems, sometimes before others realize they are a big deal. That means I can help put technology to work in a way that makes our business more efficient, which leads to better profits and happy bosses and better compensation for myself and those I work with.
Unless all you ever want to be is a low-rung developer, or if you don't have any desire to stay with the company you're with long-term; then it always makes sense to get to know your business, and it will make you a more valuable employee.