Iron golems can be used to kill blazes, but there are several drawbacks: They do get set on fire by the Blaze's fireballs, and can also take melee attacks. As with wolves, a splash potion of Fire Resistance can help. Blazes won't drop the Blaze Rod unless a player deals the killing blow.
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.