Flaming arrows don't work. The velocity of the shot will ensure that that fire won't be burning when the arrow hits. It's a Hollywood-ism :p
Not really, the arrows, javelins, or random siege armaments were wrapped in cloths and dipped in tar, used to light ships, towns, encampments, w/e on fire. This was very common.
What is hollywood is every night battle featuring arrowheads being lit on fire and fired at infantry, for cinematography reasons, like why it is always raining in nighttime city scenes.