A few years back, your product strategy would have focused on functionality and user experience, as some of its key points. It was a rare occurrence to have an API immediately available for your product, which users could have used to create interesting mashups, move data in/out and several other things. This is definitely changing.
WebWorkerDaily summarized the need for an API quite well. The post mentions that an API allows information to flow in and out of your system and creates a growing community that creates tools, mashups based on your API. An excerpt from the article, gives a good example of Basecamp:
APIs create opportunities for development beyond what an application’s creators may be able — or willing — to do on their own. For example, Basecamp is a good project management tool, but 37signals has very carefully considered what features to add; it hasn’t chosen to add every suggested feature. But there is an API for the web-based application that lets anyone create the features that they need. If you browse through just the add-ons Basecamp links to, you’ll be there for a while.
The world is indeed flat, as Thomas Friedman pointed out in his book. The same applies to products of today. They need to participate in an ecosystem where they expose that API, that allows free flow of information both into and out of the product. Of course, you can do that gradually by giving read access and then write, as you fine tune your product.
Having an API brings a lot more benefits to your product. It allows developers to consume the API and create applications / mashups that you could not have envisioned. A case in point, the number of mashups in the directory has crossed over 5000. This just shows that a lively community is out there to integrate your product, once you provide real value via your data or your functionality. Another important benefit of having an API is to let it get tested in the real world.
Further, an APIs is also a partnership tool. Services that do not have an API are potentially missing out on a larger audience. And it would be surprising if their existing customers aren't already asking for it.