If previously I described some common composite names used in Spain, here I will expand a bit to mention some common nicknames (whose closest translation in Spanish is "apodo"). In general, giving your friends or family (random) nicknames, at least as a form of endearment, is not as common a practice in Spain as in the United States. What is common is hypocorism ("hipocorístico"), that is to use the "short for" version of a name much like "Bill" is short for William, "Dick" for Richard, or "Susie" for Susan in English. This particular kind of nickname is _very_ common in Spanish.
Here is a non-exhaustive list of common "short for" names you are likely to come across while living or visit Spain (or other Spanish speaking countries for that matter):
Common "Short for" Names:
Women: Common nickname:
Men: Common nickname:
Fernando Fer, Nando
I can't help but think that some of these nicknames have become popular simply to compensate for how depressing, anachronistic, or overly religious the significance of the original full name is (e.g. Dolores, Concepción, Inmaculada).
I learned an interesting nicknaming trend in my Valenciano class recently. In Castellano, nicknames tend to come from the start of the name (e.g.Fran, Edu, Dori, Inma), whereas in Catalán they often come from the end (e.g. Cesc for Francesc, Pep for Josep, Bel for Isabel, Cent for Vicent). Not a hard and fast rule, but interesting none the less.