Crude and surely incomplete, but here's something to be getting on with:
The Dutch republic: nutmeg from modern Indonesia. Alternative sources were destroyed to actively maintain the monopoly.
The Ottoman Empire: Spices from India and Indonesia. Contested Portuguese encroachment with some success initially, destroying its trading posts on the East-African coast. The Portuguese were able to sail direct to India across the open ocean, however, breaking the monopoly (and temporarily establishing one of their own).
Russia: fur. Probably not an absolute monopoly and new-world colonization greatly diluted it, though an effective monopoly on e.g. sable, a very high quality fur, exists to this day.
Britain: slaves (to Spanish America only). The Spanish crown licensed the slave trade to its colonies (the asiento) and was forced to concede the exclusive right to Britain after the War of Spanish Succession.
Dutch Republic/Kingdom of Holland: Anything from Sakoku-era Japan. Japan granted exclusive trading rights to the Reformed-Protestant Dutch who believed only an elect chosen by God could reach heaven and therefore had no interest in missionary work which was destabilising the country.
Spain (effective): Chinese porcelain. Spain's pacific fleet took vast quantities of silver mined in Mexico and Bolivia from Acapulco to Luzon and thence to China (where it was rare and expensive relative to elsewhere). The silks, porcelain etc. bought there, of a quality without equal in Europe, was shipped back to Acapulco and on via the treasure fleet to home. I don't know to what extent they could manipulate the market, but simply no one else came close to having similar amounts of cash to spend.
Spain: various tropical goods. Spain attempted to exclude all other powers from Caribbean trade. The adventures of privateers and pirates from Portugal, Britain, France and the Netherlands are what are remembered but these were pinpricks to the Spanish behemoth.
(?) Britain: Indian cloth. Unsure, but IIRC Britain enjoyed substantial monopoly powers on cheap, high-quality Indian cloth.
South Africa: Diamonds. The de Beers diamond monopoly famously "made" diamonds as a product, e.g. paying celebrities to buy diamond engagement rings (which were never a tradition before the 1930s or so) and inserting various catch-phrases ("diamonds are forever" etc.) into the English language.
Hittite Empire: spices. The Hittite empire controlled what's today Northern Syria at the end of the trade route along the 'fertile crescent' from the East. When they lost control of this region, their empire rapidly fell apart.
Athens: Black Sea grain (etc.). Athens established a chain of fortified towns along the Bosphorus and used their monopoly on the grain trade especially as the foundation for their empire (which was much wealthier than its geographical extent would suggest).
Carthage: Anything coming from the Atlantic to the civilized Mediterranean. Hanno the navigator explored the Atlantic and Carthage spread rumours of horrors that lay there to discourage others. Naval dominance enforced the monopoly.
Anybody but Russia: Trade along the Eastern-Baltic coast. Various powers (the Teutonic Order, Poland, Sweden) attempted to seize the Eastern coast of the Baltic sea. None was ever 100% successful, but it did leave Russia disadvantaged until the time of Peter the Great.