The single biggest skill that a product manager needs to have (IMHO) is the ability to look at his product like a user would. Period.
This simple perspective isn’t really simple in reality. There are several problems. First, looking at the same product day after day for months together (and sometimes years) can make even the sharpest minds go jaded. Second, it requires the product manager to make assumptions about the user and the penalty for making a less accurate assumption (than the product manager of a competitor product) is heavy. Finally, a product manager should resist the temptation to think like the others product stakeholders (engineers, sales guys, etc.) yet work closely with them. This means, that the ability to sit on a thought island is an absolute necessity. Even if it is a marooned island in your company.
This post on skills required would be incomplete without some other basic skills. The first among them is communication. I don’t refer to the ability to make a grand speech in front of a hundred people. Here, the communication skill required is more subtle. A product manager should be exceptional at the art of story telling, and use it to make another product stakeholder see logic.
And finally, analytic skills are a necessity too. The ability to look at a large data set and make out what the numbers convey is valuable skill. Also, knowing what to measure is an important trait.
Before ending this post, the following Dilbert comic strip seems relevant here. At some places engineers are rock-stars, but for every rock-star engineer there needs to a balancing product star to keep the perspective of the user as the guiding light in product development.