Melt butter in a large skillet over medium-high heat. Stir in sugar until smooth. Add bananas and cook until caramelized. Pour rum into a measuring cup and then pour it into skillet. Stand back and carefully light rum with a long match or barbecue lighter. When flame has died down and most of rum has cooked off, spoon out bananas and sauce into bowls of vanilla ice cream.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.