It depends on what you mean by "counts."
AP exam score-- possible college credit, though that will depend upon the score achieved on the AP exam (which is taken via College Board on a single date in the spring, and costs $ to sit for). Some elite colleges in particular offer placement only, and some not even that. It's also possible that elite schools will favor students who report 5's (basically, top scores) on AP tests, but few say that they will/do. Anyone can register for and take an AP exam-- College Board really doesn't care whether or not you've taken a class. Rather like the Bar Exam or SAT that way.
AP class grade-- may/may not be "weighted" so that an "A" in that class gets averaged into a student's GPA as a 4.5 or a 5.0 (instead of 4.0 the way most A grades do) in terms of the high school GPA. Colleges do like to see top grades in AP coursework. They like to see AP coursework since that is often a mark of students who aren't trying to "pad" a GPA by taking fluff. Some AP courses require that students sit for the corresponding AP exam. Others do not.
As if that weren't complicated enough already, some high schools may have dual enrollment arrangements with local community colleges or universities, whereby an AP course can be directly taken for college credit-- earning both a high school grade and a the same time, a college grade with a regular transcript and everything.
