I had a significantly different experience than many here, as I was out for a number of years and basically ignoring the issue before it slowly occurred to me.
I still believed that the JWs had "The Truth" for many years after I quit attending meetings. However, I had always been fascinated by the tetragrammaton and how the Hebrew letters had these neat sounding names, Yod Heh Vav Heh.
Totally independent from that, I began collecting a group of friends who were nominally interested in the occult. I started by reading a couple of books about Wicca, but they seemed rather trite to me and also to be geared towards escapists. (I don't exactly feel the same way now, but I did then.) I had one friend who was studying Enochian Magick and who had also read much regarding other types of ritual or ceremonial magick. I was surprised that he even knew the name Jehovah and after picking up a book or two regarding the topic, I was even more amazed to find that there was much more to YHVH than met the eye (Qaballah, for example.). ("We're the only ones who use Jehovah's name"... right...)
As I began to study various subjects, including Taoism, Buddhism, etc., and practice, the stringent mental structure that had been embedded by the WBTS began to fall away. The relativity of our individual belief systems became apparent and the possibility of the JWs having a monopoly on The Truth became laughable to me.