Is IYTC (International Youth Travel Card) worth in Madrid? Should I have one?

I have never heard of that card. What it may be interesting is to have the ISIC (International Student Identity Card. You get 50% discount in most state museums in Spain plus travel discounts (cheaper air fares, for instance).

You also have the Euro < 26 card, which is valid in a lot of countries in Europe (not only within the EU). However, you have to be a citizen from one of those countries to get one and, obviously, you have to be under 26.