There are already some really excellent comments here. I agree very much with flyingmoose that an ideal would be that if you only knew the method names, you would still understand the API/class. Personally, I think this is something every API designer should strive for, but few ever actually reach. I also agree with dragonchild that an obsessive drive for simplicity and domain experience are two characteristic likely to be found in all good API desingers. (Although on occasion, a fresh perspective is good, not that this is mutually exclusive with domain experience, but sometimes good abstraction requires a distancing of ones self from the details of the domain.)
To these points I would like to add consistency. To me, this is an equally important element of a good API and one I strive to instill in every one I design. Consistent handling in method/function/variable naming conventions as well as in argument names and argument ordering (something I think is key to perl since it lacks named parameters). An obsessive drive to organize (a place for everything and everything in its place) is also something I think most good API/library designers have, a disorganized API can kill other positive aspects very quickly.
If you are instested in further study of API design, I would like to recommend this book. Reusable Software - The Base Object-Oriented Compontent Libraries by Bertrand Meyer, it is heavy on Eiffel (whose base libraries it is talking about), but really really insightful and smart. I believe that Eiffel actually begun not as a language, but as an attempt to "understand the fundemental structures and paradigms of software development". This book is basically about that process. It is one of the only books I have found that actually discusses the principles of good library construction in detail, including class names, proper use of inheritance, ideal class size, etc. etc. I actually keep it on my "within-arms-reach" shelf, next to the O'Reilly Perl catalog and my favorite Addison Wesley titles (Refactoring, Design Patterns, Pragmatic Programmers, etc).