A good API is one that makes simple things simple (minimum boilerplate and learning curve to do the most common things) and complicated things possible (maximum flexibility, as few assumptions as possible). A mediocre API is one that does one of these well (either insanely simple but only if you're trying to do really basic stuff, or insanely powerful, but with a really steep learning curve, etc). A horrible API is one that does neither of these well.
