Rum is distilled from sugarcane, aged in oak barrels, and usually from South America and the Caribbean.
There is a multitude of "Tiki" type of cocktails that use Rum as well as some classic cocktails. Here are a few examples of Rum based cocktails: Pina Colada, Daiquiri, Cuba Libre, Mai Tai, Zombie, and the Rum Punch.
Those cocktails are all great, but here is one that I developed myself. Give it a try:
Rumoney
1 1/2oz Dark Rum
1 1/2oz Sweet Sour
1/2oz Honey Liquor
1/4oz Lychee Liquor
2drops Angostura Bitters
Shake all ingredients and strain into a chilled cocktail glass.
For more information about Rum, check out:
Rumshop.net