Eggnog traditionally includes bourbon, rum or brandy. The drink uses high amounts of spices and sugar, so substitution of other liquors may not affect the flavor significantly.
Traditional eggnogs involve adding rum to milk, eggs, sugar and spices. This recipe derives from the Triangular Trade between Europe, Africa and the American/Caribbean colonies, which brought plentiful rum and sugar to Europe. The disruption of rum production during the American Revolution encouraged the use of other brown liquors, most notably bourbon, which still enjoys popularity today. Brandy predates both rum and bourbon as an ingredient, but it fell out of favor due to cost.