Co-Founder of CoachUp Inc., 2015 Forbes 30 Under 30 Entrepreneur, Software Engineer, Angel Investor, mentor @ Techstars
It depends on the stage of the startup. If you're talking about a green field project, then it's super important for the developer to have strong analytical skills and somewhat of a business sense (if they're going to be taking requirements from non-technical sources and trying to develop something from scratch).
If the startup is a bit more mature, then finding someone who has the 'fire in the belly' and deeply believes in what the company is trying to achieve is one of the most powerful things you can hope for in a developer (assuming they also have the technical ability to perform).
Flexibility is always something sought after as well. Startups often pivot and change directions often, so startup developers need to have thick skin when a project they're working on doesn't pan out, or the company needs to pivot in a new direction. This is why I always look for developers who understand that business needs drive development, not vice versa.