Army raiding is a risky tactic--if you hit at the right place at the right time with the element of surprise, you can cause enough damage to win. But if your opponent sees you coming, and you fight in his territory in near-equal numbers, you'll most likely lose your raid and perhaps the game as well.
The general principle of army raiding is to hit the opponent's econ in a vulnerable spot with a large enough army to deter any counterattack for some period of time. In this fashion, you kill enemy vils/caravans (or force them to garrison). If you have overwhelming force, you can pretty much stay disable your enemy's economy indefinitely. So, if you think you can win battles for some period of time in enemy territory (meaning, more/better forces), you have a good spot to raid, and you have a way of getting out of the raid, an army raid is a good idea.
Now for when you don't army raid
1. If you and your enemy have about equal forces
Assuming equal micro skill, the enemy will always win any protracted battle, because his supply line is much shorter than yours. He can also convert his villagers into militia in a dire situation.
2. If you don't have a line of retreat
Unless you are so confident that you have so much force that you'll win any upcoming battle, you should never attack unless you have a way to retreat. On maps like Old World and Amazon, army raids can be extremely risky because of the rivers and chokepoints that slow you down. If you cross a river or two and use up your ambush or force march on the way to the enemy, you run a very large risk of getting trapped and losing your entire army to a counterattack.
Incidentally, this is why army raiding on Sahara works so well; because there are usually no chokepoints, your army can always run in some direction to get out of trouble before the enemy can react.
You can view this as a special case of the general rule of war, "Don't fight battles that you can't win." This is one of the things that separates expert players from non-experts non-experts will suicide their armies in battles that they can't win, while experts will try to gauge the size of the enemy's forces and only engage if they think they can win. In general, you should always think about how you can retreat, because you might start losing the battle, and it's much better to retreat and save some of your troops to fight another day than to have your entire army wiped out.
3. If your enemy can immediately attack an important frontline city
Let's say I'm Turks and you're Bantu. You army raid my first city with your entire army. I won't even bother trying to counter it; I'll just make 3 siege factories, take your frontline econ city with six siege weapons and my main army, and you won't be able to stop it because your army is totally out of position.
Here are a couple games to illustrate some army raiding principles. In the first, Suckaaa gets trapped while army raiding on Old World--he has no way to retreat, and while he kills a few villagers, this is more than offset by losing most of his raiding force. Lesson don't army raid without a line of retreat. In the second, Suckaaa army raids with about equal forces; again, you can't win an army raid with equal forces because the enemy's shorter supply line will kill you. After killing most of his raid, I go on an army raid myself, because I know that I have (for the moment) overwhelming force to stop any counterattack, which lets me disable his second city for a while until I can get to IV.