I have encountered quite a few APIs which are both poorly supported and not well thought out. There is a lot of emphasis placed on supporting the product but as a developer I want the API to also be a first class citizen in the support priority queue. Take a look at Salesforce APIs. The documentation is horrid, the APIs are not very good and sometimes even broken (like with Desk.com), and there is little to no support. Customers for a product get support, but what about developers who aren't customers but are essential for building out the platform for your product?
I want everyone to be like NetDNA when it comes to their API. For example they went and joined a hangout to help someone out with their API.