Like others have said I think it really depends what you want to do.
I would love to to work on the visual part, editorials, layouts, design (fonts, colors, graphics, etc.). I think my dream job would be doing fashion editorials but I want to have a broader background so I can work with other aspects too. So I'm majoring in Visual Communications at an art school just so I have a strong knowledge and ability to use the concepts such as balance, color, gestalt principles, spatial principles, storytelling with imagery, as well as the Adobe creative suite, and be able to draw! My school doesn't have a fashion program but I think if your interest is strong enough and you keep up with it as much as you can, that won't be a problem.
Also like BetteT said there are many ways, but no one surefire way to get a job at a magazine, so I think interning is so important. To give you experience and contacts.
And also it's true (just from what I've heard from other tFSers) that you can make it without a degree if you are driven and ambitious and know the right people and are good at what you do. I just think I'd feel naked or have an insecurity if I tried to start a career without getting a degree. Plus education never hurts.