Minecraft wiki entry for Defeating_the_ender_dragon, associated text: Slow falling potions are helpful, because they negate the fall damage of the dragon’s knockback ability. However, a bucket of water can serve the same purpose. Because of the slow fall, you also have more time to react in case your are kicked off the island, so you can save yourself with an ender pearl.
Night vision potions can be nice to have, because the end is dark and it helps you see better. However, end stone's bright texture contrasting with obsidian, endermen and the dragon's darker textures makes this optional, although you may confuse the voids' darkness with enderman.
Strength potions boost your melee damage against the dragon and endermen.
Leaping potions and swiftness potions can be used to boost the player's movement during the fight.
Poison potions and harming potions can be used to damage the dragon when it perches down or in the air.