In general, one can group the heraldry of the Spanish kingdoms into three: those of the Basque and Navarre regions, the rest of Spain and the New World.
In the Basque & Navarre regions in the north of the Iberian peninsula, heraldry is inspired by nature and has some motifs that are found in the arms of the families, town, etc. Animals, birds, trees and stars are very common with certain species more so than others.
It is especially common to find an oak tree as a principle charge as Basque towns usually had a large one in the town center where the inhabitants would meet to discuss matters of importance. Kind of like the modern town halls or the Athenian Agora.
Just as common as the oak tree is the wolf. Wolves used to be a major plague in Europe up until about a century or so ago. Especially in regions where mutton was a staple food, wolves would literally eat the food of the locals. This is why one sees wolves as charges on the shields in the Basque & Navarre regions.
On the other hand, the more southern parts of the peninsula is inspired by symbols, local scenery and the wars against the Moors. Perhaps the most common charges are castles, lions, bordures and Moors themselves.
The use of a castle or a lion more often than not allude to a descent or origin from the homonym kingdoms of Castille (castle in Spanish) or Leon (lion in Spanish).
What is, to me at least, very interesting is the use of specific bordures to commemorate a battle. Those who participated in the battle of Las Navas de Tolosa use a bordure with 8 crosses fleury, those in the battle of Baeza use 8 saltorels and those who participated in the battle of Salado use the motto Ave Maria gratia plena.
When it comes to the New World, a whole new selection of possible charges entered Spanish heraldry. All of the local fauna and flora were possible charges, from llamas to corn to potatoes to indigenous symbols, all were used by the conquistadors. It is said that the Spanish heralds of the 17th and 18th century treated the blazon as secondary part of the coat of arms and went crazy with the new designs. Designs that today we could call lucky charmish.