The first one I remember running into was the movie "Little Nemo". I watched it when I was just a little guy (somewhere around 4 or 5), and while I liked it, I thought it was just a cartoon. Years passed, and I forgot about it. One day a few years ago, for some reason or another, a memory from it popped back into the forefront of my mind. I had forgotten the name and it was driving me nuts, wondering exactly what it was.
At some point, the possibility of it being an anime crossed my mind, since the movie seemed a tad off the beaten path when compared to typical American animation. A few months ago I posted here on the BxT Forums inquiring about it, and indeed, it turned out to be an anime. I then proceeded to get myself a copy and post it on the BxT tracker.
Another one was Sailor Moon. Once again, when I was young I saw an episode or two on TV at somebody else's house. I thought it was just another cartoon, but its art struck me as unusual (it's why I remembered it), and years later when I got interested in anime I figured out that it, too, was an anime.
EDIT: Oh yes, just remembered a more recent one: The Galaxy Express 999 movie. I had watched part of in on the SciFi channel some time in the late 90s/early 00s, thinking once again it was "just a cartoon". It sprung to mind a year or so ago, and upon investigation found that it was an anime.
