Thanks Carl V!
Yes, the use of artillery as a constant weapon in battle starts with Gustavus Adolphus, who essentially invented light cannon, light enough to move around with an army and not slow it all down. The Russians invented horse artillery which made it mobile enough to use, and Frederick the Great got his hand on every piece he could.
This is why I distinguish Medieval and ancient, where its use was rare -- the Romans and Byzantines, who were great engineers, used them, but they were rarely a 'big deal' in battle. They simply took too long to set up, so could be used mostly for known set-piece battle.
My point on cannon, thought, whether it was Frederick of Gustavus, is that cannon tends to be a direct fire weapon once the battle started, although thinking of it as 'bombarding' can be correct for pre-battle conditions. It rarely fired from behind when the owning's side's troops were advancing because its trajectory wan't reliably high enough. The exception was, of course, when the cannon could be placed at elevation. Then, they could 'bombard' enemy troops a la Civ III. Indeed, this was and could be so devastating that it rarely happened since most defending commanders weren't dumb enough to let it happen. So, when Washington dragged the cannon to the heights outside of Boston, the British just withdrew instead of fighting and de facto committing suicide.
My point is that cannon DID participate in battle starting with the 17th century. They sometimes bombarded enemy troops at a distance; Napoleon, of course, was very good at this. They had longer range than hand held guns and could bombard set defenses. However, their range wasn't like modern artillery, and once the battle started and your own troops moved forward, its more accurate to view them as direct fire units, and shouldn't be able to bombard form safe distances. Cannons were often captured and/or spiked.
By the time of the US civil war, cannon really didn't have much more range than a rifle, and cannon was most effective defensively (so they could fire at enemy troosp advancing without hitting their own troops) firing cannister, meaning that the cannon was essentially an overgrown shotgun. But they could be tactically decisive, they were powerhouses. So, my take is:
Ancient artillery, sometimes used in battle but it was at most a support arm, important in sieges
Medieval -- Rarely used in battle, but Medieval warfare was dominated by sieges anyway and or course artillery was important.
Gunpowder -- Cannon used tactically in battle, either light cannon of the Swedes or horse cavalry. Very important, but a bombardment type model is probably less accurate than a direct combat arm. Because of the nature of defense, a 'free bombardment' shot may be realsitic if attacked.
Modern -- Fires at long distance, behind the lines. Bombardment is perhaps appropriate (although I dislike how dominant it was in Civ III).
As Karl V points out, the examples he uses are essentially set battle areas, artillery is devastating. So, in WWI, with trench lines, artillery is the dominant weapon and does bombard. As he pointed out, battles like Sevastopol, where there is time to set-up, again, artillery is dominant.
In WWII artillery probably caused most of the casualties, although tanks and aircraft may have passed artillery as the decisive weapon. Why? Because tanks mobility allowed them to breakthrough to the support areas in the rear where the artillery is vulnerable. The Germans used tanks to break-through and surround. The Russians, however, were masters of artillery, and often tried to pin the Germans to devastate them with the big guns.
So, now (since the end of WWII), to add mobility to artillery, we have self-propelled artillery ....
Breunor
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