I know this sounds a bit morbid, but writing about Madonna on her birthday is like writing about Michael Jackson after he died. When someone was so omnipresent though most of your childhood, but you could never call yourself a fan, it's hard to conjure some sort of personal anecdote -- she simply was. And is. I don't remember a pre-Madonna existence.
I must have been around nine or ten when I first became aware of Madonna. At the time, I thought the world was divided into Cyndi (Lauper) and Madonna girls, and never the two shall meet. I was a Cyndi girl, and that was that.
By the time Madonna's music and especially her videos become more about art and less about dance pop (though always inherently danceable), I had cultivated a distain for pop music and moved on to punk and indie. (Cyndi girls usually go punk.) I only came around during college, when I should have been slamming to Pearl Jam and Nirvana. The music of the early 90s was so dark and plodding it was hard not to feel suicidal just listening to it, and I needed a serious shot of glamour. I can only link to these, but here are a few of my favorite Madonna videos from that era.
Deeper and Deeper
The Power of Good-Bye
Take a Bow