Can you drink the hotel room water in Spain?

Spain is not a third world country and potable water regulations have been passed within the EU. I cannot see drinking the water in a hotel is any different to drinking the tap water elsewhere in a city. Your problem, if any, will be to do with what you are used to, where it is sourced and therefore taste. I will be surprised if the water all over Italy tasted the same.

Yes, the water in Spain is great.
You can drink it from most public fountains too, unless they have a sign on the fountain that says you can't.

Yes, it is. Water is totally safe and it complies with all the water regulations, which are very strict. Wherever water isn't potable, as said earlier, there'll be a sign saying so -some fountain and pumps, especially in remote locations.

However, taste might be a factor. This is a map of the water hardness in Spain. As you can see there are many areas, especially along the Mediterranean coast, where the water is either hard or very hard. This is mainly caused by the presence of dissolved bicarbonate minerals in the subsoil of this part of the continent. This gives tap water -which has obviously passed all regulations- a characteristic chalky taste, well, not chalky but sort of. You'll soon understand why the conditioning shampoo and decalcifier industries (the later for washing machines, dishwashers... ) are so important here :)))

This, of course, is not to say that you might find spots here and there that get their water from caves with less concentration of minerals and therefore has less taste.

I spent 89 days in Spain this summer. I drank tap water in every hotel room without ill effects. Once or twice I noticed a mineral-y flavor, but certainly nothing like the taste of the (dreadful) tap water here in Washington DC. If you're lucky enough to have an in-room refrigerator, you'll find that cold water usually has less of an odd taste.

I asked the same question in 1979 when I lived in Paris and was visiting New York. I even called the New York water authority to see if I could use tap water for my baby's bottles. It all seems funny now. You'll think so too once you get to Spain.

And those lovely big ice cubes in the cold drinks.

THanks everyone.
Very glad to hear that I won't have the same concerns as when travelling in Mexico.
Michele