Nashville numbering is yet another way of transcribing songs. It can be found, along with Chord Pro, chords, and tablature, on the OLGA website, although with diminishing frequency.

The system was invented by Neil Matthews Jr., one of the Jordanaires (Elvis Presley's backing band) as a way of transcribing music so that it can be transposed easily to accomodate singers' varying vocal ranges.

Simply put, a song is transcribed with the numbers of the intervals placed where the chords would be.

As an example, here is the first part of the Barenaked Ladies' Hello City, transcribed in Nashville Numbering:

I         IIIm
Another night at the Palace,
IV IVm I
'cause there is nothing else to do
IIIm IV IVm
Whoa whoa, whoa whoa
In this example, if the song is played in the key of G, then the chords would be G, Bm, C, and Cm. Transposition is thus made easy, if you know your scales or even just your patterns if you're playing guitar. You would then know without thinking that if the song was in A, the chords would be A, C#m, D, and Dm.

Roman numerals are used so that nonstandard chords like sus4 and 7th chords can be used. Otherwise, you might see "34" and wonder whether it meant the 3rd chord in the scale with a sustained 4th, a 3rd and 4th chord played in quick succession, or the 34th chord in the scale.

The standard tonality of the chords are sometimes ignored; III could signify a minor chord (which is the usual case in a major scale) or a major chord (since there is no 'm' marking); it would be wise to double check this with the bandleader.

One also sees case used to signify tonality; the major scale would thus be represented I - ii - iii - IV - V - vi - vii.


Sources:

http://tinpan.fortunecity.com/melody/73/nashville.html
http://www.google.com/search?q=cache:HRVgQBhEj3c:www.guitarweek.com/nashvill.htm+nashville+numbering&hl=en
http://www.alanhorvath.com/LSN5.html
http://www.musicbooksplus.com/books/hl370.htm