I've had an on-and-off love affair with classical guitar for almost two decades, and I would like to share some favorite pieces.
Concierto de Aranjuez ("That's the Concert of Orange Juice to you!" and a cookie to whomever gets the reference), by Joaquin Rodrigo
"Gran Vals" by Fransisco Tarregá. Now if I could only get that bit at 0:13 as a ringtone....
"Asturias", by Isaac Albeniz.
"Fantasia para un gentilhombre", by Joaquin Rodrigo. Written as a gift for Andres Segovia, whom apparently didn't think much of "Aranjuez".
"Sakura" - Trad. played by P-O Kindgren. Yes, I know it's a koto piece originally, but... just listen to it!
edit: wrong link to "Aranjuez". Oopsie...