Another of my passions in Madrid. I live close to the center and my parents always took me to walk there, I am lucky enough to know some quite typical places.
One of them is Casa Labra, located in a historical building since it is where the Spanish Socialist Party was created. The place is not very big and although it has a restaurant part, it is actually famous for the "tapas" of cod, croquettes and banderilla in pickling brine.
The place is typical and traditional so that it is quite full most of the time, especially on weekends so I recommend being patient. During the week it is possible to find a free table but the rest of the time you will most probably have to eat your tapas standing.