Heraldry
If you are interested in learning whether or not your ancestor bore arms, I can research this for you. To be fair, you should know from the outset that your chances of finding an armigerous ancestor are better if you have an ancestor who once brought a hidalguía lawsuit as described below, or held officer rank in the Spanish army or navy before 1834, or was a member of one of the knightly orders. To know this, you will need to research your family tree first, so heraldry research usually comes later.
Although Spain is a Kingdom, there is no official heraldic authority to whom petitions for arms can be addressed. Beware of individuals masquerading as such on the Internet. Don Vicente de Cadenas, Spain's last generally acknowledged Chronicler of Arms, passed away in December 2005; even the legitimacy of certifications of arms offered by him is questionable, as shown for example in this message regarding the College of Arms in London's assessment of the legal value of Spanish certifications of arms. There is no reason to believe that King Juan Carlos will ever appoint anyone else to oversee Spain's heraldry.
British subjects of Spanish descent may contact the College of Arms or the Lord Lyon to enquire about a grant of arms. If you live in a country with its own reputable private heraldic organisations, such as Germany or the United States, you may want to consider registering arms of new creation there: I will be happy to work with you in researching known arms for Spanish lineages that share your surname, if you would like this new creation to reflect your Spanish heritage by bearing similar but not identical motifs.
Spanish heraldry presents a number of particularities that make it different from that of England or other European nations. In my opinion the most important is that generally Spanish heralds have not followed the practice of differencing, that is, placing a small mark on each person's arms to distinguish their bearer from his or her father, brothers, first cousins and so on. This means that over decades and indeed centuries identical arms may end up being borne by individuals who have the same surname yet are very distant cousins. But make no mistake about one thing:
SPANISH ARMS SYMBOLISE A LINEAGE, NOT A SURNAME!
Beware of unscrupulous merchants trying to sell you "bucket-shop" arms, ie. any arms for Sánchez or Martínez or any other surname that have just been plucked from a heraldic dictionary. In Spain all arms can be borne undifferenced by any male-line descendants of the first grantee. But to legitimately use those arms, you must to be able to trace your descent from that grantee.
Many people are interested in searching for their ancestors' arms, if any, simply as a way of adding some colour to their research; the arms may be displayed on a chart or emblazoned on a banner or some other personal object. Published works on Spanish heraldry will be of little or no use in such research, because they very seldom give the full name or geographical location of the grantee, only a surname. There is no central institution in Spain analogous to the College of Arms, either. Traditionally the records kept by each Herald were considered his personal property, to be perhaps passed on to a son who would carry on the profession; the records' survival rate is, therefore, uneven. The best sources for heraldic information today are the entry records for Spain's knightly military orders, in Madrid; other sources include the pleitos de hidalguía, lawsuits brought by non-titled noble or gentry individuals seeking recognition of their status and prerogatives. There is but a handfull of books linking arms to specific individuals, such as the Conquistadors of Spanish America.