Today's web application world is much different from a couple years ago, and dramatically different from the 90's. Most major companies would have agreed in the 90's that a closed system was the way to go.
Today, most startups and even some corporations are shifting towards open systems. A lot of the "web 2.0" sites have boosted their success by allowing their data to be free and spread out. Software becomes much more powerful when we adopt the open source mentality into the web applications we create.
Flickr's API is an example of how it's done. My Moo cards were very easy to order and edit. To me, Google's Map success is not based on it being the best mapping solution available. However, by providing developers with an incredibly simple way to create maps, the web has embraced it.
Recently, developers have built some really cool apps on top of Twitter, especially the Twittermap, a strangely entrancing google map and Twitter mashup. We are coming to a time when it's nice to share and it makes buisiness sense to share. E-commerce is another great example of where API's make sense. Amazon has been able to spread it's content throughout the web, give a small percentage through affiliates and make more sales.
One major issue that stands in the way of major API adoption is widespread monetization. The conventional wisdom seems to be that if you it gets you more subscribers or traffic - great! There seems to be a lot to learn from Amazon.
