Yes, they did, and there are several good reasons why they did so. Eventually, Europe transitioned out of this sort of warfare as technology changed.

If you want to know why people stood in lines to shoot at each other, you have to look backwards in history. Formation fighting has existed for as long as we have records of history. We have stellas from mesopotamia showing armies with helmets, armored cloaks, shields and spears marching in big formations, and this method of fighting can be found almost everywhere in the world since then.

So why did people fight like this? The first rule of warfare is to outnumber your enemy. It doesn't matter if your opponent has 10,000 guys on the battlefield and you have 1,000, if his soldiers comes 10 at a time, you're going to crush him. Formation fighting lets you put a lot of people in a small space such that they can protect each other and gang up on anyone who attacks you. Formation fighting also gives you the confidence to march into a fight where you may be mangled or killed. It's important to note that standing in lines to kill each other isn't the exception, historically it's the rule. The real question, is when did people stop standing in lines and why didn't the stop earlier?

People stood in lines in the 1700's because guns weren't deadly enough. 10 guys couldn't outgun 100 guys, so if you hid 10 scattered about, I could rush you with my 100 guys, drive you from your position, disorganize your forces, scare the rest of your dudes, and you could in an absolute best case scenario, kill 10 of my guys. And probably less than that. So lets say you have 100 guys scattered about in a field trying to be all tactical. Remember what I said about being outnumbered before? Since my guys are massed up and yours are spread out, I will outnumber you and outgun you anywhere we fight. Guns did not have the range, fire rate or accuracy necessary for your spread out guys to kill my massed up guys. Your position is even worse if I have cavalry. My cavalry can move quickly enough that you'll be lucky to kill even 1 of my guys before I'm on top of you.

During the 16th, 17th and 18th centuries, while formation fighting was the rule, there was still room for skirmishing musketeers. For example, in the battle of Lutzen (the one in 1632 not the one in 1813), the commander of one army placed a bunch of musketeers in a depressed road and used it as a trench to delay an army of swedes. These skimishers didn't stop the enemy, or even kill a bunch of them, but they did delay and confuse the other side. Earlier in that same year, there was the battle of Alte Veste, where the wing of one army was taking cover on a hill in trenches and a castle, while the other wing was standing in lines in an open field. But in general, you couldn't count on having such cover to protect, and sometimes it would cause problems. In 1512 (this is super early in the development of firearms, but the lesson is sound) in the battle of Ravenna, the spaniards fortified their camp with a trench. The french simply flanked the fixed position and bombarded it with enfilading fire to devastating effect. Worse yet, the Spaniard's own fortifications got in their way in the subsequent cavalry duels. While the fortifications helped the Spaniards against the french infantry, the Spanish were unable to pursue the broken infantry, allowing the french to regroup, surround them with the help of the french cavalry, and crush the spanish.

Here we can see that infantry under cover can be used to great effect to delay the enemy, but it will not stop a determined foe and a fixed position makes you very vulnerable to flanking. Open field combat with massed formations lets you bring incredible amounts of firepower onto the enemy, as well as freely reposition to avoid a flank, withdraw from an undesirable fight, or pursue a broken enemy. In addition, massed formations of infantry were necessary to fight off cavalry. If the terrain you were standing on was not sufficiently rough as to prevent cavalry from charging, you could easily be run off the field because they would outnumber you in that fight.

Throughout the earlier part of the 18th century, massed tactics prevailed, and skirmishers were used sparingly. According to Delbruck, the Prussians (who were a preeminent military power of that time) despised the use of skirmishers because they brought little pressure against the enemy in the attack. European armies of that time had achieved such skill in their training of infantry, that they could push through a harassing screen with little effort. Or so they thought. During the Napoleonic wars, all of the major powers realized that skirmishers could be incredibly disruptive against enemy formations if properly deployed in large enough numbers. The idea was that the skirmishers would disrupt the enemy's formations and fight off their skirmishers, then your line infantry would assault through and push the enemy into a route. Massed lines were still important on the assault, but skirmishers were invaluable.

As the 19th century wound on, gunfire became more and more deadly. With the invention of the minnie ball and then of breachloading rifles, gunfire became so deadly that even a small number of soldiers could inflict incredible casualties on an exposed enemy. Artillery preparation and rapid assaults were necessary to minimize the time exposed to enemy fire and push through their lines. By the time WWI started, infantry hit the ground as soon as the shooting started. If they feared artillery, they dug holes for themselves and hoped for the best. The line of battle was long dead.

Sources:

"The Military Revolution" Geoffrey Parker

"Battles of the 30 years war" William Guthrie

"Warfare in the 17th century" John Childs

"History of the art of war" Hans Delbruck

"Infantry Attacks" Erwin Rommel

"Achtung Panzer" Heinz Guderian

I hope this isn’t too off topic, but I wanted to give a different perspective on the idea of eighteenth century warfare, from a North American colonial perspective. Native American warfare with the very same European weapons was markedly different from the Old World battles of massed volleys, open battlefields, and little emphasis on marksmanship. For an interesting discussion of the colonial context at the same time you should check out Patrick Malone’s “The Skulking Way of War: Technology and Tactics Among the New England Indians” (2000) and Armstrong Starkey “European and Native American Warfare 1675-1815” (1998).

Basically, Malone and Starkey argue that Indigenous peoples of the North America were more well suited to use seventeenth and eighteenth century firearms with a greater degree of accuracy than were their European counterparts. Natives adapted to the usage of muskets very quickly as they were natural marksmen, adept hunters –good eyesight, fast reflexes – and years of experience with the bow and arrow. In the seventeenth century, quickly overcame any sort of reluctance or hesitation for using this new technology.

The English colonists on the other hand, Malone argues, were poor marksmen and in spite of the promises of New England being “a land of plenty,” did not have success in hunting much else than waterfowl. The deer and the wolves of the New England forests were wary and timid animals, which proved too great a challenge for the average colonists. However, aside from these embarrassing hunting trips, the European colonists had little use for marksmanship as they had mastered the technique of “the massing of firepower” to a devastating degree (as mentioned in the previous posts regarding continental warfare). The simultaneous discharge of all the muskets could indeed cause devastating carnage if directed towards a tight formation of enemy soldiers. The volley, however, was only effective if both formations massed into similarly tight formations.

Indigenous peoples did not fight cohesively but placed individual skill, marksmanship, and valour above strict European discipline and drilling. An Aboriginal warrior, having been trained in marksmanship of hunting animals all of his life, would take a well-aimed shot at his opponent, possibly firing multiple balls to increase the likelihood of a casualty (not a technique commonly used in conventional Old World warfare). Starkey has also commented that native warriors made good use of the vegetation and of their terrain to execute ambushes. Once combat had been joined, they continued to use the terrain for cover and to execute complicated flanking manoeuvres or withdrawals. As Starkey argues, Indigenous tactics resembled more closely to modern army tactics than did their European counterparts of the eighteenth century. Malone famously argued that “the colonist had brought the firearm to the New World… [but] the Indian would demonstrate how to use this machine.”

I hope that this isn’t too off topic and perhaps provided interesting insight on how a different kind of people used the exact same technology to engage in a very different kind of warfare on the other side of the Atlantic.

I am a PhD student researching French-Indigenous colonial encounters, diplomacy, and alliance making in the eighteenth century.

I'll add a few comments to /u/tyn_peddler excellent post concerning muskets.

Part of the reason behind the linear tactics is the slow rate of fire of muskets. Since reloading was a slow process, the officers wanted to make sure soldiers didn't waste a volley by firing at beyond effective range. If the men are dispersed in cover, it's hard for for an officer to control their fire.

They're in a line because that puts the most guns online but is unwieldy to move. Whereas a column with a much smaller frontage can march much faster but can only put a fraction of their muskets into use. So drill became important because it allowed you to move hundreds of men quickly from a line to column to charge the enemy, or from column to line to put out a maximum amount of fire.

Another reason behind the linear tactics were the inherent inaccuracy of the musket - they'e smoothbore guns so tend to lose accuracy quickly. So to insure the maximum amount of hits you mass as many guns as you can in a small area - that's why the men are shoulder to shoulder. They're a living shotgun in a sense.

As a side note, that is also the logic behind the colourful uniforms. There's a reason behind the British with their red and French with their Blue uniforms. Because everyone was using black powder which produces a huge amount of white smoke, prolonged firing would result in your soldiers (and the enemy) disappearing into these clouds. The colours would help generals spot and identify their forces. Consider how much smoke is produced from a few rounds of fire by a relatively small amount of men. Now imagine several tens of thousand firing as rapidly as they can and add in cannons.

They also did this in the American Civil War in 1860. They had much more advanced weaponry then than they did in the 1700's. But still, they stood in lines and fired. Which is also why it is the bloodiest war for America still, to this day, with almost 700,000 casualties (given some of these people died from disease)