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. Niccolò Machiavelli lived in and wrote about this period in The Prince and Discourses on Livy. 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 centred 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 sex slaves). It was referred to as a "mixed republic", with a monarch-like doge (who lost much of his powers over time), a Senate and a Major Council made up of key aristocrats, the latter being the real ones in charge of the country. Eventually invaded by Napoleon, the Austrians took all its foreign possessions in the 1797 Peace of Leoben. 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.
The Republic of GenoaThe 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. Nice Job Breaking It, Hero?
PiedmontNow 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. 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 realising 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? The capital of Savoy/Piedmont/Sardinia/Whatever was Turin.
San MarinoThe only Italian city-state republic of the Renaissance 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. 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. (You may have noticed a glaring omission from this list of major Italian cities. For the region ruled from Rome in this time period, see The Papal States.)