My own personal exposure to category theory mostly consists of reading the following blog entries:

- The entire beginning of <a href="http://unapologetic.wordpress.com/">The Unapologetic Mathematician</a>,
- Todd Trimble's <a href="http://topologicalmusings.wordpress.com/2008/06/22/basic-category-theory-i/">series on basic category theory</a>,
- Random weeks of John Baez's <a href="http://math.ucr.edu/home/baez/TWF.html">This Week's Finds</a> (unfortunately it is somewhat hard to search these).

I won't claim that this is at all a systematic or comprehensive way to learn category theory, but I do think there's some genuinely good writing here and that it's gotten me comfortable with category-theoretic language, even if I wouldn't actually say that I "know" category theory (whatever that means).

**Edit:**  Also, though I've only read the beginning, Lawvere and Schanuel's <a href="http://books.google.com/books?id=o1tHw4W5MZQC&printsec=frontcover&dq=conceptual+mathematics&cd=1#v=onepage&q=&f=false">Conceptual Mathematics</a> is probably the simplest introduction to category theory I've ever seen.  I think it was written for an undergraduate course.  To get an idea of the level of this text relative to some of the others mentioned here, adjoint functors are never explicitly defined.