From today, the Thyssen museum in Madrid, one of the 'golden triangle' of art museums in the capital (along with the Reina Sofia and the Prado), has free entry every Monday from 12noon until 4pm.
The move means that now all three museums have free entry at some point during the week. The other two museums have at least two hours per day, every day, to visit their exhibits for free. See exactly when they are open for free here: Golden Triangle Art Museums in Madrid
All three museums feature in my list of the 100 Things to Do in Madrid