The Cranky PM started it by describing different programmers from a product managers view. Ran Arad jumped in with his characterization of product management. He suggests that there are only two characteristics to consider:

• Has technical skills = (True/False)
• Knows what he wants = (True/False)

(Knowing that some product managers can't understand Boolean logic, he also provides a handy chart.)

For another view, see The Product Manager (in the movie Office Space)[NSFW]

Whenever I talk about The Strategic Role of Product Management, I discuss the importance of understanding the technology as well as the business. Many companies split product management into two parts, non-technical and technical (ie., the top and bottom of the Pragmatic Marketing Framework) but this organization style often fails.

No two ways about it: you need to be technical to be a product manager for a technical product.

Instead, most companies evolve to a left-right orientation of product manager and product marketing manager. The product manager is responsible for finding and quantifying market problems; the product marketing manager focuses on taking the product to market. Both roles require technical competency.

For more on roles, download my free ebook, The Strategic Role of Product Management.

Update: Paul Young at ProductBeautiful adds to the discussion in How Technical Should a Product Manager Be?