Mojito is a traditional Cuban highball. Traditionally, a mojito is a cocktail that consists of five ingredients: white rum, sugar, lime juice, soda water, and mint.

Caffeinated alcoholic cocktail made of cola, lime, and dark or light rum. This cocktail is often referred to as a Rum and Coke in the United States, Canada, the UK, Ireland, India, Singapore, Australia and New Zealand where the lime juice may or may not be included.

Piña Colada is a sweet cocktail made with rum, coconut cream or coconut milk, and pineapple juice, usually served either blended or shaken with ice. It may be garnished with either a pineapple wedge, maraschino cherry, or both. The piña colada has been the national drink of Puerto Rico.

Coquito is an coconut-based alcoholic beverage traditionally served in Puerto Rico. It is generally made with rum, coconut milk, sweet condensed milk, vanilla, cinnamon, nutmeg, and cloves. https://en.wikipedia.org/wiki/C…

Dark 'n' Stormy is a highball cocktail made with dark rum (the dark) and ginger beer (the stormy) served over ice and garnished with a slice of lime.

The Mai Tai is a cocktail based on rum, Curaçao liqueur, orgeat syrup, and lime juice, associated with Polynesian-style settings. Wikipedia

Hurricane is a sweet alcoholic drink made with rum, fruit juice, and syrup or grenadine. It is one of many popular drinks served in New Orleans.

Firecracker Cocktail is an American classic savoury July Fourth drink consisting of rum, syrup, Peychaud’s bitters and absinthe, and garnished with three red grapes.

Of Thread and Theory Cocktail is a cocktail that originated from Georgia and widely popular in America. It is prepared with rum, bitters, apple cider vinegar and sorghum syrup

Fish House Punch is a strong, rum-based punch containing rum, cognac, and peach brandy. The drink is typically served over an ice block in a punch bowl and garnished with lemon slices.