At least in the Java world, good APIs are very rare. The vast majority of the APIs I’ve used in Java are at best mediocre, and I’ve run into some real stinkers (No fingerpointing here, but a lot of them are even in the standard library!).
Part of this is the fault of the language. Java code… tends to be ugly. It’s not a language which lends itself to really flexible syntax, and so you have to work really hard to produce powerful abstractions which are actually nice to use.
The only APIs I’ve encountered so far which have really made me sit up and go “Wow, that’s well designed” are Google Guice and Joda time. They have well thought out class hierarchies, good object oriented style, sensible use of fluent interfaces / method chaining and just generally well thought out interfaces and names.
They’re not perfect by any means, but they show promise that it really is possible to write good APIs for Java.
Anyone else know of other similarly well designed libraries?
 And, unfortunately, I lack much in the way of non-trivially large development in other languages. The Parsec API is nice, ‘though it gives me a headache sometimes. Haskell libraries in general look rather pretty, though I suspect that’s more a function of the language than the API design. I’m not really experienced enough in it to judge good API design.
 I’m not an OO fanatic. It has advantages and disadvantages, and sometimes you just want to use a different approach (I rather like FP for example). But one thing I’ve observed is that if you do it right, OO can have the effect of producing some astonishingly readable code. I don’t know either well/at all really, but this style of design seems much more common in Ruby, smalltalk, etc.