Recuerdos de la Alhambra is probably the most famous piece by Francisco Tárrega, known as "the father of classical guitar". It means "Memories of the Alhambra" referring to the moorish palace complex in the hills of Granada in Spain. It is quite a technically difficult piece to play, requiring a good right-hand technique to play the tremolos (fast repeated notes) evenly and consistently while allowing the lower arpeggio notes to sing. Below you can see a graphic video of the music, play the mp3 file or see the sheet music score before downloading. If this piece is beyond your skill level on guitar, then for an easier piece by Tárrega try his Lagrima (meaning "Teardrop").
Here is a video of Tárrega's Recuerdos de la Alhambra for guitar:
The audio controls below allow you to play the music or download Tárrega's Recuerdos de la Alhambra for guitar as an MP3 file.
The image below is the first page of the sheet music, and here you can download the full sheet music for Tárrega's Recuerdos de la Alhambra for guitar in PDF format.