I'm planning on visiting Spain for several months. Is the Amex (American Express) brand credit card well accepted? Is Visa or Mastercard more accepted than Amex?
As an Spanish inhabitant and an AMEX card holder, I can say that most stores are reluctant to accept American Express nowadays.
In a big city such as Madrid maybe 25% of the places would accept it, but if you go to a smaller province capital city, you will be lucky if 1 out of every 10 venues accepts it. You can look for the blue square sign, as Itai says, but sometimes there won't be any in your surroundings.
Important note: almost every taxi accepts Visa and MasterCard, never AMEX. So remember to withdraw some cash if you want to take a taxi. The same applies for most bus lines. Long-distance train, however, accepts AMEX.
While acceptance has grown, American Express is much less accepted than Mastercard or Visa. We had trouble in Spain getting it accepted and learned that Mastercard worked much more often.
Now, you can choose to go to establishment that accept American Express which is often shown as a blue sticker on the front door of such places. If you choose the place first, it seemed that most typical established not of a high-end nature, do not take Amex often. Again, it depends where you go. Places that aim for a business-type clientele, are more likely to take it.