I like a lot of the stuff already mentioned in this thread but here's a little blurb about my first times listening to this kind of music.
I'll mention both ambient and post-rock because there is a lot of crossover.
I remember the first time I heard Ambient music and the first time I heard Post Rock. Both were beautiful experiences. The first ambient was an album called "Beyond the Horizon" by Streamline. I must have been in junior high at the time. I didn't really know what it was but I loved it. Google searches don't ever tend to yield anything but they still have the albums on iTunes.
As for post rock, one day in junior high we had someone come to our class to get our feelings on a selection of songs. One of the songs was "Rockets Fall of Rocket Falls" by Godspeed! You Black Emperor. I was so in awe that I approached the man after the presentation ended and he gave me the cd he played. Once again, didn't know what I was listening to, or that it would be my passion one day, but here we are.
Currently Listening To:Every Little Step - Bobby Brown