The history of Santa Lucia is complex- a Neapolitan folk song, transcribed by Teodoro Cottrau (a classically trained musician), the music commonly heard is a revision of the folk tune by A. Longo (a classical musician known for his revisions of Scarlatti sonatas). The words most commonly heard, those sung by Caruso, "Sul mare luccicica....," credited to Cottrau and Longo (spelling at the ingeb site linked by Sorcha is correct). The Caruso recording is available on several websites.

The following is one Neapolitan folk song version. There also is an Italian 'translation' which I will post tomorrow.
If anyone can translate the Neapolitan, please post!

Lyr. Add: SANTA LUCIA
(Neapolitan folk song)

Comme se fricceca
la luna chiena...
lo mare ride,
Il'aria è serena...
Vuje che facite
'mmiez'a la via?
Santa Lucia!
Santa Lucia!

Stu viento frisco
fa risciatare,
chi vò' spassarse
jè pe' mare...
E' pronta e lesta
la varca mia...
Santa Lucia!
Santa Lucia!

La tènna è posta
pe' fá na cena...
e quanno stace
la panza chiena,
non c'è la mínema
melanconia!
Santa Lucia!
Santa Lucia!

Pòzzo accostare
la varca mia?
Sanya Lucia!
Santa Lucia!

Midi and mp3 (very slow!).
The website has 549 canzoni napoletane!

Index to songs beginning with S- http://www.medivia.it/italiano/canzoni/canzoni.asp?lettera=s
S

Lyrics Index, letter A:
http://medivia.sele.it/italiano/canzoni/index.htm
Santa Lucia