Synesthesia affects approximately 1 in 25,000 individuals. It seems to be a genetic disorder (or gift as the case may be) as it runs in families. In the US the ratio is about 3:1 female to male synesthetes, while in Britain is is 8:1. Synesthetes are predominantely left-handed1.
Vladimir Nabokov was synesthethetic. For instance as a toddler he complained that the colours of his blocks were "all wrong". Both his mother and his father were synesthetes, so Vladomir undoubtably received the condition from one of them.
Electronic musician Richard D. James (a.k.a. Aphex Twin, AFX, Polygon Window, etc.) is a synesthete2. This fits the music he makes as most of his songs and albums seem to have a dominant "colour". For instance, Selected Ambient Works Volume II is decidedly brown, which is also the dominant colour of the album's cover, which Richard designed.
Another possibly synesthetic artist is Syd Barrett, early guitarist and songwriter of the band Pink Floyd. Barrett, however, was also a painter and used classical and free jazz music to inspire his paintings. Andrew King, one of the band's managers in the late 1960's, said of Barrett's song "Interstellar Overdrive":
It was all very much part of Syd's approach not to separate things into categories. He saw art and music as complementary ideas and he was always trying to get his music to sound like his art and visa versa.3
Syd Barrett's synesthetic experiences may have come from LSD. His use of the drug was well known, and is said to have caused him to "freak out" permanently to a degree that he was kicked out of the band by the other members.
It's possible that everyone is a little bit synesthetic. Use of drugs such as LSD or mush, and some other psychedelic drugs can bring on synthestetic effects. However, there's no need to go to those extremes to get an idea of what it's like. Just close your eyes and think of the number one. Does it have a colour? Now, think of the number two. Then three and four. What colours are they? Most people associate a definite colour to each number, and the colours you associate can be used as a crude personality test. The Lüscher Color Test by Dr. Max Lüscher is one example, which is described in a book of the same name. This is a mild synesthetic effect.
You can also try this with music. Listen to some good, complex, instrumental music. (I would recommend Aphex Twin or Squarepusher, but that's just me). As you listen to the song, ask yourself "what colour is this chord?" or "what shape is that drum beat?" Electronic music is good for this as it often deals more with raw sound than form, melody or lyrics as much pop music does. For me, a song like Squarepusher's "Beep Street" conjures up shades of blue and green in the bass melody. The treble melodies are orange, yellow and red and the drums explode like white firework flashes. But that's my personal interpretation, and it's probable that you will see something totally different. YMMV.
If I had to have a mental abnormality, I'd go for this one.
1 Richard E. Cytowic "Synesthesia: Phenomenology And Neuropsychology"
http://psyche.cs.monash.edu.au/v2/psyche-2-10-cytowic.html
2 Aphex Twin Artist Information, Warp Records Website. http://www.warprecords.com/.
3 Cliff Jones Echoes 1996 Carlton Books.