Counter to flaming arrows...

[kianduatha]

Storm, Mist, Rain, Arrow Fend, proper positioning of shielded troops to affect who the AI targets with the bows, flying troops with attack archers to tie up the archers, any battlefield-wide spell like Rain of Stones or Earthquake or even something like Foul Vapors.

[LDiCesare]

That and darkness and fire resistance spells, or Will of the Fates and the like. Army of gold should be quite good but it's pretty late game.
Depends on your nation and magic research. If you're in a hurry against a given opponent, you may want to provide specific details to see what can be used fastest, otherwise any of the above would help.