Preheat the oven to 350°F. Line muffin pans with paper liners. Paper liners help ensure the muffins don't stick to the pan and make for easy clean-up, but if you don't have any, grease the muffin cups instead.
In a large bowl, mix together the eggs and sugar until well combined.
Add the mashed bananas, vegetable oil, vanilla, and cinnamon; stir until well combined.
In a medium bowl, mix together the flour, baking powder, baking soda, and salt until well combined.
Add the flour mixture to the banana mixture. Mix gently just until the flour mixture has been incorporated (this helps keep them fluffy; over-mixed batter makes the muffins dense).
Spoon the batter into the muffin cups, filling each one ¾ full. Don't overfill the cups, as the batter may spill out onto the pan as the muffins start to rise.
Bake for 17 to 20 minutes or until a toothpick inserted in the center comes out with a few moist crumbs (or clean) and no wet batter. For moister muffins, I like to take them out when there are a few moist crumbs on the toothpick.
Allow the muffins to cool in the pan for 5 minutes.
Carefully remove the muffins from the pan to wire racks to cool completely.