On Saturdays admission to the Casa de lope de vega (C cervantes) is free (only open in the morning I think). Lope de vega lived here (surprisingly!) in the first half of the 17th century and it's furnished with genuine artefacts of the time. You have to do a guided tour with a guide: they claim not to speak English, but ours did. The best thing is being able to handle real 17th century books, which we have never been able to do before. (Perversely, Cervantes lived in C. de lope de vega, which runs parallel to c cervantes). Also, next door is a very cheap place to buy churros and .... other things (to eat!).

On Sundays, admission to El Prado is free (but not Saturday afternoons as stated in the 2003 Rough Guide); but it's free for children all the time (as is the adjacent Botanical Garden).