I started reading comic in the 1970's, so my earliest memories of her were from her feature in the anthology book Superman Family (where she was an actress in a soap opera in her secret identity), and from the reprints of her Silver Age stories in the old Adventure Comics digests. I also read pretty much every issue of her series from the early 80's (where she moved to Chicago and went back to college; weird, but I remember what happened in her personal life more than the actual action in those comics). I mourned her death in Crisis, but at least she went out in a blaze of glory.
I followed the post-Crisis version of Supergirl, but really became a fan of that version during her late 90's series, where the Matrix version merged with a troubled teen and became an "earth-born angel". (Fun story: about ten years ago, I was trying to put together a proposal for an updated version of "The Forgotten Heroes" that I was gonna submit to DC, and this version of Supergirl was one of the lynchpins. But they rebooted their continuity around the same time I gave up the delusion that I stood a chance in hell of starting a career writing comics in my late 30's, so that was that....)
Funny story: The drugstore around the corner from where I live started carrying comic books again for the first time in over a decade about three months ago. (Pretty much all Nu52 titles, with a couple of Archies thrown in, but still, new comics!) They've slowly been expanding on the number of books they carry, but among the first few? Supergirl and Justice League United. :)