Tuscany is perhaps Italy’s best known wine region and home to Chianti, the most important in terms of volume. Traditionally Chianti was required by law to contain a significant percentage of white wine (between 10% and 30%). In addition to the Sangiovese and Caniolo grapes, they were forced to include Trebbiano and/or Malvasia. 
In theory, this would soften the wine, making it more approachable early on, and increase its aromatics. In fact, the huge yields of these added white grapes diluted the wine, making it thin and dramatically increased the wine’s acidity, throwing it out of balance. People worked from both within and without the system to correct this. 
Those who worked outside the system felt that they should make the best wine possible, regardless of the regulations. After all, their name was on the label. This often meant making a wine entirely from red grapes that couldn’t be called Chianti. In most cases, they used the now extinct ‘Vino di Tavola’ or ‘table wine’ moniker. This was the lowest classification, similar to the jug wine category in the U.S. 
Many of the "Super Tuscan" wines were wildly successful, and some sold for even higher prices than the finest Chiantis. To accommodate them and give them formal governmental approval, the IGT category was created (Indicazione Geografica Tipica). Today, the ‘Super Tuscan’ designation has as much to do with aging in French barriques as the grape choices.
Other winemakers felt  compelled to work within the system to effect change, in many cases to uphold the multi-generational traditions of their family. Change came slowly, but today, a wine can have up to twenty percent Cabernet Sauvignon, Merlot or Syrah in the blend and still be called Chianti Classico (as long as the grapes are from that region).

The trend today is towards higher percentages of Sangiovese, the result of isolating superior clones of that grape and matching it to the growing conditions of the specific vineyard sites.
The difference between Chianti and Chianti Classico is one of geography. The Classico area is the heart of the region and is considered to have the best vineyards.   

Additional Info

Other Wines of Tuscany:

Brunello di Montalcino - The grape is a Sangiovese Grosso clone named by its color when ripe (little brown one). It is considered to be one of the best reds of Italy. Made popular by Biondi-Santi, who held tastings for the wine press featuring very old (up to 100 years old) bottles of Brunello, the wines fetch some of the highest prices of any wine in Italy.  Rosso di Montalcino is also 100% Brunello, but typically from younger vines and made to be drunk sooner.
Vino Nobile di Montpulciano - Based on the Prugnolo Gentile clone of Sangiovese, it is considered to be between Chianti Classico and Brunello di Montalcino in quality.
Carmignano - Another Sangiovese based wine with mandated portion of Cabernet.
Morellino di Scansano - Made from at least 85% Sangiovese, this grape was named by the clone’s color when ripe, thought to be that of a Morellino cherry.
Vernaccia di San Gimignano - A white by the grape of the same name, this was mentioned by Dante in his Divine Comedy. The wine can be a bit peppery with bitter almond notes, but still with refreshing acidity.