Most online methods of making money involve writing, whether it is via Adsense, product sales, email marketing, etc. It's typically not a question of "do I need to write content" but "how much" and "what type" of content you need to write.
The only real sites that make money without lots of written content are usually 1-page or 1-feature sites that go viral. Sites like
rainymood or
instantrimshot where it is just one page with one simple feature that is easy to use, with ads on the side.
An expanded version of those sites would be sites like
fmylife, which don't actually publish content but just provide a platform for others to publish content. Even though this site probably has thousands of pages of user-generated content by now, the main attraction that made it viral is once again just one single easy-to-use feature that people enjoy using.
My advice if you are looking for passive income (isn't everybody) is to either suck it up and write content yourself, pay someone else to write content, or focus on creating and marketing a single-page/single-feature type of site like the ones I have mentioned (then monetize with ads or whatever). If you have an idea for one of these single-feature sites but lack the programming/html skills to make it, you could even pay someone else to develop it for you.