The natural way is the best way and it certainly isn't out of the question even in highly competitive niches. Search engines are gearing more towards high-quality, feature rich content more than ever and the old saying "content is king" is more relevant now than ever. What better way to have regular visitors sharing, liking, following and discussing your content, than great content?
The real question is not how to build backlinks, but how to increase exposure so that your backlinks build themselves. Think about it this way: a backlink is seen by a search engine as a sharing, or liking, of content. The whole idea of a backlink is that it gives a user the ability to navigate to your web page. Backlinks exist so that human beings may share content with one another, not for search engines. The Google algorithms are designed around this fact; Google follows users, users don't follow Google.
With this in mind, it's important to realise that the only reason backlinks are important is because they give a very accurate estimation to a search engine algorithm the general perception of a piece of content's quality. In other words, the more backlinks a community is giving you, the more said community must think your content is good. So, again with this in mind, the question is not how to build links yourself, but how to increase your exposure so your links build themselves.
There's no single answer, no magic bullet and no one-size fits all answer. Techniques range from link exchange, social networking, paid links, forum signatures, real life advertising, but most will only get you so far. Some really great techniques include:
Guest posting on other peoples' blogs to prove your worth
Interviewing - either being interviewed or interviewing someone with a reputation (this might not be free)
Social networking is very important, building relationships via FB, Twitter, Google+, etc.
Multimedia networking, i.e., YouTube videos, etc.
Competitions, where you give something away for free - always attracts people
Sponsoring others that are related to you (normally not free)
Editing Wiki-style pages with citations to your website
Flyers and business cards develop word-of-mouth promotion
Local listings, online listings and directories
There are so many ways to increase your exposure so I won't post much more than this, but really my opinion is to not focus so much on manually creating all your links and have other do it for you, the way it was meant to be.