Most places allow photography, except some museums or old buildings. Also, if pictures are allowed, be sure to ask if that is "con flash" o "sin flash" (with/without flash) Many places do not allow flash, but do allow pictures so be sure to know how to turn off the in-camera flash.

Just from what I can remember, the following are:

Prado Art Museum, Madrid: Pictures, no flash allowed. No video allowed. (I was surprised)

Palacio Nacional, Madrid: Pictures, no flash. Video allowed.

Monastery @ Santo Domingo de Silos: Pictures with/without flash allowed, video allowed, except in small art gallery room. No recording the monks, either.

Guggenheim Museum @ Bilbao: No pictures at all, no video.

If I am informed correctly, the police in uniform and military do not allow photos taken of them while on duty, though i don't know if this is true.

I've never had trouble taking photos anywhere, I just remember to ask every museum,etc. "Se permite sacar fotos?" o "Se permite grabar en video?"

And I'm with the other replyer, keep the gypsies with twigs who "tell fortunes" away. They are pickpockets, along with the people who want you to "sign their petition". Good luck.