++ [ originally posted by Kaiser Franco ] ++
Fiorentina are actually called "i viola", i.e. the mauve (players). It's a common mistake among foreigners to think that "viola" applies to the team when in fact it applies to the players, like "bianconeri", "nerazzurri" and what not. So there's no such thing as "la viola".
These are just names describing the team colours though, as many teams will have their own particular nickname.
A few that come to mind :
Milan : il Diavolo
Roma : la Lupa (the female wolf)
Genoa : i Grifoni (the griffins)
Inter : il Biscione (the big grass snake)
Napoli : i partenopei (a reference to the old Roman name of the city, a bit like Marseille who call themselves "les Phocéens")
Torino : il Toro (the bull)
Palermo : i quaquaraquà (ok I made that one up, that's mafia talk)
Last but not least:
Juventus : la Vecchia Troia, Rubentus, i gobbacci, le seghe...etc