On my first visit to Madrid (in 1997) I spent a few hours wandering around - it's a very low-rise city. I wanted to get into the Royal Palace, it has free entrance on a Wednesday if you're an EU citizen, but you need to be able to prove that fact - and I forgot my passport - so they wouldn't let me in.
My second visit to Madrid (in 2004) was a little more successful - I remembered my passport, but I was there on a Monday, so I had to pay 9 to get in. You can't win them all. The palace is worth the price, some of the painted ceilings are amazing, and the chandeliers aren't bad either!
I was there just before Christmas, and the Christmas market was in full force on the Plaza Mayor - selling any bit of Christmas paraphernalia you could image.