The best known influence is the existence of many arabisms (words with an Arabic origin) in the Spanish language and toponymy. You can find many examples of that in this article from the Cervantes Institute (it's in Spanish, mind you):

http://cvc.cervantes.es/lengua/biblioteca_fraseologica/n1_cantera/lexico_02.htm

For obvious reasons, it's specially important the number of arabisms that start with 'al-' (or 'a-' after the disappearance of the 'l') such as: alcázar (castle), albaricoque (apricot), alcalde (mayor), albañil (construction worker), alfil (bishop in chess), albóndiga (meatball), etc.

In the toponymy, you can find the rivers Gualdalquivir and Guadarrama, among others; the province of Guadalajara; towns with the words Alcalá or Calatayud in their names, or places that begin with Beni-.

Also, there's a widely used interjection in Spanish that comes from Arabic. Ojalá (I hope, let's hope, hopefully) comes from the expression insha'Allah, meaning "if Allah wills".