There is a Standard Italian, that follows the rules of Italian pronunciation. The majority of Italians, though, speak one particular Regional Italian - that's to say a recognizable local variant of the language.
I prefer to talk about a variant and not a dialect for two reasons, firstly that Regional Italians differ in only in minor traits, namely lexical choice, pronunciation and tense choice (phonology, morphology and other aspects of grammar are the same as Standard Italian); and second, that there are indeed Italian dialects (or rather, languages of the Italian family), but they are different beasts.
Lexical choice
The same concept is realized with different Italian lexemes.
For example, the concept of NOW is realized as ora South of the Appennino Tosco-Emiliano, and adesso North of it.
The two words are completely interchangeable, and practically all native speaker of Italian will understand both (they are true synonyms in a denotational sense, like soda/pop); but a given speaker will almost always have a definite preference for one.
There must be close to one hundred of these lexical choice points. Interesting isoglosses can be drawn. Some more examples:
- string beans: cornetti in Lombardy, fagiolini everywhere else.
- folder: carpetta south of the river Po, cartelletta north of it.
- cheese: cacio in Tuscany and parts of Central Italy, formaggio elsewhere.
Pronunciation
Like in English, the same word can be pronounced in different ways (you can take a look at the Italian pronunciation node). For example, the word tre (three) is pronounced /tré/ in Northern Italy and /trè/ in Central and Southern Italy.
The R phoneme has many pronounciations; in Piedmont it is close to the French R of rouge. In other parts of Northern Italy it is an indistinct vowel sound,almost like a schwa. In Sicily again it is very characteristic.
In the same manner, in parts of the country the sibilant S turns into a sounds not unlike the SH in "show". Bologna is a typical example.
Some minimal couples do not survive in the Regional Italians: for example the Parmesan variant pronounces pésca (peach) and pèsca (fishing) exactly in the same way. The same things happens with rosa; in Standard Italian, the word with a sibilant S means "rose", and with a voiced S it means "gnawed" - but many regional variants either invert the sounds or pronounce both in the same manner.
Tense choice
Northern Italy eschews the simple past (io feci: I did) and prefers the present perfect (io ho fatto: I have done), while Southern Italy does the reverse.There are indeed rules for Standard Italian tense choice, but they are obeyed only in some parts of Italy, like Tuscany.
All Italians, though, recognize and understand all the tenses - because they are taught in schools and used in literary Italian.
These phenomena should not be confused with other tense choice issues, like the progressive substitution of the subjunctive by the imperfect indicative; other forces are at work here, like social class and education.
How do Regional Italians come into being ?
After the birth of Italy as a unified state, in 1861, an national school system was imposed. The language taught was, and still is, Standard Italian; the language of Dante, Petrarch, Alessandro Manzoni, Gaspara Stampa and the other greats of Italian literature.
But at that stage, Italians did not speak Italian: most spoke an Italian dialect (the royal family itself, the Savoia, spoke mostly the Turin dialect and French).
School and other unifying forces, like cinema, newspapers, radio and television, superimposed a layer of Standard Italian over the bumpy, quirky landscape of Italian dialects. Regional Italians are the result of this superimposition.
Standard Italian, on the other hand, is more or less the dialect of Tuscany. Now Tuscanians will foam at the mouth here, but the linguistic truth of it is that the Italian you read in Italian literature is more or less the Tuscanian dialect as spoken by the middle class in Florence, minus a very small number of lexical traits. This is why, when you go to Tuscany, it seems like "the region with no dialects": it has one, and it has become Standard Italian!
As to why this particular dialect acquired so much prestige - it really boils down to the moment when Dante decided to write the Divina Commedia in the volgare (Tuscanian dialect) of the time, and not in Latin (even though he was an accomplished writer in that language). Dante wanted widespread diffusion for his poem. Dante's work stands at the center of Italian literature, and it is written in the Tuscanian dialect; most other great writers and poets followed in the tradition. The extreme was probably Alessandro Manzoni, doing a deep revision of I Promessi Sposi (The Betrothed) to insure its conformity to Tuscanian norm.
Before Dante, though, and for a while before, there was a heated debate about what kind of language should a unified Italy (the idea was there for many centuries before the country itself) speak. Certain Sicilian dialects were also strong contenders at the time.
Recognizing Regional Italian and the Impossible Speaker
A given person will have a set of lexical choices and pronunciations. This set can be associated with a certain place with very good accuracy. For example, I can detect if someone comes from my hometown or from places about 10 miles away from it. I like to speak (borrowing a term from information theory) of this recognizable set of linguistic traits as a syndrome. Normally one can recognize the syndromes from his hometown and surrounding places: for more distant places, one can more or less locate the general area. As a speaker from Parma, I can discriminate among Piacenza, Reggio, Bologna and Modena. But all the Sicilian dialects sound alike to me.
Occasionally, foreigners will learn Italian from more than one teacher. This turns them into "impossible speakers": you can't have Brescia's clipped prosody AND Turin's "R" AND say "ora" instead of "adesso".
Is a regional accent a cross to be born in silence?
To begin with, it is not a cross at all; since most people have one, it is just a feature. Anyway - it is possible, through intense training and great care, to rid yourself of your original regional Italian and speak Standard Italian. This is normally taught in acting schools; some people that do that are TV and radio speakers (even if recently the state TV started tolerating mild regional accents), and politicians.