Joelle Renstrom, writer and writing professor
I agreed with the other answers here. Writing is a broad and multifaceted discipline--there are so many different types! While most classes tend to require a particular type (a thesis-driven essay or a research paper or whatever), any and all writing you do will help your other writing. If you're a dancer, learning ballet would help you with tap; tap would help with hip-hop; hip-hop would help you salsa. Each dance focuses on rhythm, timing, and strength, and those skills would be improved regardless of which style of dance one practiced.
One major piece of writing that doesn't get enough attention is critical thinking. Before you put a word on the page, you have to have something insightful to say. Critical thinking doesn't come naturally to a lot of people, so it's yet another skill to learn and practice. All kinds of writing rely on critical thinking--analytical papers, certainly, but also poetry and fiction-writing. One has to think critically about how best to tell a story, which point of view to use, which details to highlight, how to make the dialogue work. The more you can hone your critical thinking skills, the better you'll be as a writer in any genre.
Creative writing allows you to tell a story, which in turn gives you greater insight into how others tell stories and why they use whatever techniques they do. That kind of insight is a tremendous help on research and analytical papers. It goes the other way, too--if you analyze a writer's approach to a topic, that likely would affect the way you would choose to approach a topic creatively.
Another benefit is that you'll develop style and voice regardless of what type of writing you do. Malcolm Gladwell famously said that it takes 10,000 hours of practice to master a skill. Suffice it to say, it takes a lot of practice to get really good at writing--the good thing is, writing in any genre is practice.