In addition to normal weapons, Blazes can be hurt by snowballs, taking 3 (1 1/2 hearts) per hit. If they have found a way into the Overworld, they are also damaged by water and even rain: Water does roughly 1 damage every second. Like all Nether mobs, they are not damaged by fire or lava.
Using bows and arrows to fight Blazes has been quite common among players. Players can increase the damage caused by the ranged attack by enchanting the bow. If players use level 5 Power enchantment on their bows, they will easily be able to kill these mobs with two hits.