For much of its history, Italy was a geographic expression. Before 1861, Italy was a collection of city states and principalities, frequently a target for foreign powers. Many of these weren't actually monarchies, but republics ruled by a collection of oligarchs. The city states were mostly rich and concentrated (relying on trade), centres of art and culture, a little like Dubai without the sand.
Some of them were:
You Ain't Nothing But A Hound, Doge: the Most Serene Republic of Venice aka The Venetian Republic (697 - 1797)
This state centered on the city of Venice, but owned mainland territories in the modern day countries of Greece, Slovenia, Croatia and Montenegro. Once even ruled Cyprus (the war for which was the backdrop to Othello). Had a large merchant fleet, a powerful navy and controlled a lot of trade to the Middle East for much of its history (including silk, spices, and slaves).
The city-state was famous for its Murano glass as well as its silk weaving industries, but perhaps the most important industrial site in the city was its arsenal, a shipyard which could churn out hundreds of vessels in a matter of months using early assembly-line techniques which were literally centuries ahead of their time. Of course, the arsenal's production methods were kept as an absolute secret, aided greatly by the fact that it was built on an island which was off-limits to foreigners and even most Venetians.
It was referred to as a "mixed republic", with a monarch-like doge (who lost much of his powers over time, and no, not that one), a Senate and a Major Council made up of key aristocrats, the latter being the real ones in charge of the country.
Sadly, Venice declined as a major power once alternative routes to the East were found (especially the route around South Africa, at the Cape of Good Hope), and as trade and investment flowed towards the Americas and away from the Mediterranean. The Venetians fought (and mostly lost) several wars with the Ottomans, and lost most of their possessions in the Eastern Mediterranean as a result. By the very end, Venice had degenerated into a gambling center, an association still noticeable in places like Las Vegas or Macao today.
Eventually invaded by Napoleon, the Austrians took all its foreign possessions in the 1797 Peace of Leoben. Despite some attempts at rebellion, the Venetians never regained independence and were later absorbed into the unified state of Italy.
A key contribution to the study of European history comes from Venice - the state archives have pretty much all the diplomatic correspondence and ambassadorial reports, containing warts-and-all descriptions of the courts of Europe, their rulers etc.
Fun Fact: We owe the word "pants" to Venice, sort of. The word derives from the name of a popular stock character in Italian comedies named Pantaleone. The name Pantaleone identified him with Venice due to St. Pantaleone (the name means "all-compassionate") being a popular saint with the Venetians. The comedic figure was a silly old man who wore tight trousers over his skinny legs, leading people to identify the clothing with the character, leading to the term "Pantaloons", which were shortened to "pants" in the 1840s.
Florence (1115 1532)
Greatly seen as one of the great centres of the Renaissance, the other being Rome, Florence was the hometown for many if not most of the masters of the Renaissance.
Much of Florence's reputation came from the generous patronage of the Medici family, bankers whom, through well placed bribes and great shows of wealth and prestige, basically ran the city. It reached its apex under the patronage of Lorenze il Magnifico, unfortunately a combination of his generosity bankrupting the Medici bank and the timidity of his descendents slid Florence into a decline that led to a brief domination of Florence by the French and a later restoration of the old republican government. However, the Medici's had the last laugh as the Pope (Who was a Medici) granted the title of Duke of Florence and later, after the capture of Siena, Grand Duke of Tuscany.
It is because of Florence's Legacy that it was chosen to be capital of a united Italy in 1865 until the final capture of Rome six years later.
The Republic of Genoa (1096 - 1815)
The other Italian trading republic to survive until the French Revolutionary Wars (Lucca and San Marino were also republics but weren't known for trade). It was originally a four-way thing between Venice, Genoa, Florence and Pisa, but the latter two ended up becoming parts of other monarchies. Genoa was naturally The Rival to Venice and was also ruled by an elected Doge. Not only Christopher Columbus came from here, but Genoese traders were the first ones who (inadvertently) first brought the Black Death to Europe from their trade posts and colonies in Crimea.
Genoa possessed the island of Corsica for many years, but failed to put down a radical republican independence movement led by Pasquale Paoli - so they gave up and sold the island to France. The French succeeded, but in the process Corsican revolutionary ideas and a certain Corsican named Napoleon Buonaparte spread to France. Of course the result was the French Revolution and the General Bonaparte who was instrumental in conquering Italy for the French Revolutionaries, who overthrew Genoa, proclaimed a revolutionary Ligurian Republic. After the Congress of Vienna, the region was merged with the Kingdom of Piedmont-Sardinia.
Fun fact: Speaking of pants, jeans derive their name from the city of Genoa. The durable cloth used to make these pants derives from the fabric used by Genoese sailors to cover the goods they stored on the docks.
Piedmont (or Sardinia or Piedmont-Sardinia or the lands of the House of Savoy) (1324 - 1861)
Now pay attention, because this is about as confusing as Britain Versus the UK.
There's this former Italian state that was one of the most powerful and indeed was the one that ended up uniting the country in the Wars of Italian Independence. So why is nobody ever quite sure what its name is? Piedmont is the approximate name of the region it ruled, in the top left corner of the Italian peninsula. The word roughly means "Foot of the Mountains", which is accurate, as its habitable territory consists largely of the foothills of the Alps. Savoy is the name of the royal house which ruled Piedmont at the time and that of a nearby region which (even more confusingly) said royal family traded away to the French as part of a Batman Gambit during the wars of unification along with Nice. Therefore, the House of Savoy didn't actually rule Savoy at the time they united Italy. This state is also often called the Kingdom of Sardinia, the reason for this being that the Dukes of Savoy obtained the island because it gave them a royal dignity (the right to call themselves Kings rather than Dukes). They looked on it as very much a consolation prize (they actually wanted Sicily, and did briefly possess it before realizing that Sicily was too hard to govern from the north, so they swapped it for Sardinia). Sardinia did come in handy during The Napoleonic Wars, however, when the French conquered Piedmont (as in the bit on continental Italy) and the royal family (the aforementioned House of Savoy) fled to Sardinia, which was only part of the Kingdom of Sardinia, but now the only actual part that wasn't conquered. Confused yet?
In spite of the confusion, the most important figure to come from Piedmont (let's just call it that for these purposes) was Camillo Benso, count of Cavour. He was the mastermind of Italian Unification, although he died before the project was complete. Cavour was, in many ways, Italy's Bismarck. Although he was only the Prime Minister of Piedmont and not the King (again, like Bismarck, who was a Chancellor), he was pretty much in charge of the kingdom's affairs. Cavour took it upon himself to industrialize Piedmont, largely by exploiting Sardinia's resources, building railroads and encouraging factories, with the aid of British loans with which to build infrastructure. Once he had built Piedmont up enough to be able to project military force, he sided with the British, French, and Ottomans against Russia in the Crimean War. This had the effect of gaining an ally in the form of France's leader, Napoleon III (not to be confused with Napoleon Bonaparte, his uncle.)
With Napoleon III, Cavour was able to fight Austria and acquire most of Northern Italy (save for Venice). In return, Piedmont had to surrender Savoy and Nice to France, a bargain which still left Piedmont with far more land than it had before the war. With victories in Southern Italy, the unification of the country was nearly compete, but sadly, Cavour died after falling ill (probably with malaria). Nevertheless, Italy was united about nine years later, with Venice and Rome joining the country which Cavour (and Garibaldi) had largely built out of the various regions.
The capital of Savoy/Piedmont/Sardinia/Whatever was Turin.
San Marino (301 - present day)
The only Italian city-state to survive to the present day practically unchanged. It escaped the French Revolutionary and Napoleonic Wars because Napoleon admired it, considering it a model of good governance. Due to its sheltering Garibaldi during the wars of unification, the Kingdom of Italy honored its wishes to remain independent, as did Mussolini. As is traditional for Italian republics, it elects its leaders on very short terms, a matter of months. Bizarrely it was also the first place in the world to democratically elect a Communist government, and the Communists dutifully stood down when they were voted out a few years later.
The Kingdom of the Two Sicilies (1811 - 1861)
Basically Sicily and all of Southern Italy, the Kingdom of the Two Sicilies was by far the largest of the pre-unification states and, arguably, the poorest. Its capital, Naples, was the third largest city in Europe in the early 19th century but the kingdom itself was poor and underdeveloped and a byword for corruption and poor rule. The royal family were a branch of the Bourbons, the dynasty that still reigns in Spain and Luxembourg but never achieved much popularity in Italy. In 1860, the kingdom collapsed in the face of Garibaldi's invasion.
It was only officially known as the "Kingdom of the Two Sicilies" after The Napoleonic Wars, but that had been used informally as a name for many years previously. Part of the reason why it had a poor record in war was because it had been a bargaining chip in many of the wars between the great powers and its people were indifferent towards defending their king - because he was probably a foreigner who'd been installed twenty years ago and wouldn't be any different from the one they'd be given by whoever won the war.