I loved the supernatural element... not necessarily the alien side of it (which clearly dominated the story) but those episodes about all things weird and wonderful. I remember a particularly memorable episode (The Post-Modern Prometheus,, the fifth episode of the fifth season) which featured the Cher song, Walking in Memphis. Every time I hear that song, it always takes me back to the X Files. It was such a weird one, wasn't it? I loved the eeriness of it. It was just so cool.
I still listen to the theme tune, it's a particularly inspiring piece of music, especially when I'm writing an eerie scene.
Were you an X Files addict?