I think the best way to answer is to list the characteristics of good web APIs instead of citing examples. If you like Twitter/Facebook/etc APIs, what aspect of these APIs do you find attractive?
I'll take a first stab:
- Well documented APIs, including constraints and usage policies. This enables rapid development with confidence, instead of second guessing what the parameters might mean, and what return values are.
- Technology/language agnostic APIs. Good APIs should be easily usable, providing the same functionality, across a wide array of languages and platforms.
- Well supported APIs. There are always bugs. Responsive maintainers result in more usable APIs
- Layered API sets. When APIs are neatly layered, a wide range of developers can consume the pieces they need without needing to pull in extraneous layers. As a plus, it forces the creators to think hard about clean and componentized APIs.
Please add more to comments.