The job boards on Gumtree or Craigslist are full of gigs that offer "your byline" or "building your portfolio" as compensation. Thing is, unless you agree to ghostwrite for someone, you should get your byline anyway. As for the portfolio, you can demonstrate your writing skills on a blog or write for a charity. If you write for other people or businesses that intend to monetize your work, they really should pay you for that, shouldn't they?
Yes, they should. Unless they offer you a share of their user base and/or influence. Links to your website from their blog, a mention (with link) in their newsletter, listing you as a contributor on their website. This is only of value to you if the company is well-established and enjoys the trust of its user base.
You still have to make sure said user base stays on your site. A cooperation with someone in your niche would work. If the traffic your partner drives to your blog results in a high number of bounces, you've worked for nothing.
Under the right circumstances, writing for free might work. Make sure you get something in return other than a byline.