Bring 3 cups water and sugar to a boil in a saucepan, stirring mixture constantly. Pour into a large bowl; add lime juice and next 4 ingredients. Cover and freeze 8 hours.
Process frozen mixture in a blender or food processor until slushy.
Dip margarita glass rims into water; dip rims in sugar. Spoon granita into glasses.
Note: For a nonalcoholic version, omit liquors, and add 1/2 cup fresh orange juice.