Answer: Yes... but not as much as you might think.
You've probably heard that most college students change their major at least once before they graduate. Some, however, change their major over and over and over again, which can lead to extending the amount of time in school and, consequently, the amount of debt accrued to afford those extra classes.
I see this most often accompanied by the mindset that "I don't want to do Career X anymore, I want to do Career Y, so I need a different degree." I want to share some thoughts to break apart the assumptions that underlie this kind of thinking.
First of all, take a look at some job postings in your intended field. Many jobs will not specify an exact type of degree you must have, but will instead require "a bachelor's degree in business, communication, or related field" or something equally vague. That's because oftentimes a hiring manager doesn't know exactly what they're looking for, or they don't want to limit their candidate pool too much by being overly specific.
Some professions, like being a computer programmer or a nurse, do require specialized training, but many, many of the jobs out there do not map exactly to a particular college major. And there are new jobs being created all the time that do not have corresponding college majors because they haven't even been defined yet.
Second, many people change careers at some point in their life. This doesn't always require going back to school to get a completely new degree. If needed, you could get a master's degree in your new field (the threshold for what kind of bachelor's you have going into a grad program tends to be even lower than when getting a job), but really, you may just need one training course or a certification program to get up to speed in a different field.
Finally, your job experience will quickly become more important than your degree. A bachelor's in any field can help you get your foot in the door with an entry-level position, and from there you will have the opportunity to learn new skills and take on new responsibilities within your company. Once people see what you're capable of, your exact field of study becomes far less important, and you can then develop a track record for successfully completing the kind of work you want to do. In some fields (such as graphic design and editing), you can take on freelance work to build your portfolio regardless of your field of study — or lack thereof.
If nothing else, remember this: The most important thing is that you can articulate the applicability of your degree. If you can explain well — whether in a cover letter or an interview — how your course of study has helped prepare you for a position, then the official title of your major matters little.