Weaponry to facilitate movement was far more common and standard; but I need to impress upon you that there were plenty of instances of stalemate-esque warfare occurring in WWII that would be in-line with our common image of WWI.
Two immediate examples:
Battle of Normandy; during the June-July period the battles in the American sector where very much akin to a 1915 stalemate, replace "trenches" with "Bocage" and the image would be similar indeed, minus the compartmentalized battlefield. The stalemate was only broken after a series of incredibly narrow pushes that concentrated great firepower in narrow spaces.
First Siege of Tobruk; a lack of fuel and firepower prevented the initial Panzer units from breaking through the perimeter in any significant depth, and as a result a state of siege soon developed. The battles became infantry and artillery focused, with tanks taking on a support role as these forces fought over entrenchments and resistance nests from April to November of 1941.
There's many, many more examples but I'll cut it there.
I'd say that the most important difference between the world wars is not technology nor even firepower, but rather the ability to move firepower at a far more rapid pace through a breach. In WWI during the period of 1915 to early 1916, when a breach of the line was made, exploitation could only occur at a marching pace or at a trot, not fast enough in most instances to create an unfixable hole in a main line of resistance. Local, or Operational reserves would often be able to get into position moving along interior lines and retake the lost position through rapid counteraction, or establish a new line of resistance.
By contrast, in WWII, a combination of attrition, military deception and economy of force led to forces often being unable to retreat or counteract fast enough to deal with a clear-cut hole in their line. The German dash to the sea in May 1940, the American and British pincer movements in August 1944, the German retreat into the Vosges, and the destruction of Army Group Center in Summer 1944 are all prime examples of what happens when Strategic and Operational reserves are either too weak or too slow to stop the exploitation of immediate gains by powerful and mobile forces of Infantry, Artillery and Armor. Full fledged flight, or grand envelopment ensues.
See my post below for a good overview:
In short, even within the context of WWI, trench warfare was on the way out by 1917. The addition of modern, sophisticated Close Air Support, paratroopers, tanks that could reliably move in combat conditions over 2mph, reliable trucks to ferry troops across the battlefield, and advancements in artillery doctrine and methodology allowed offensive dynamics on the tactical level to be very successful.
I'll be the first to admit it's an oversimplification but when firepower is much greater than mobility you end up with trench warfare. And this is basically what you had in WWI. Tanks and aircraft were either not invented yet or still in their infancy meanwhile the machine gun and rapid fire artillery had achieved unprecedented advancements.
WWII, on the other hand, saw much greater advancements in motorized warfare that could overwhelm or outflank machine gun and artillery positions.
The factors that the existence of trench warfare were not to do with tactics so much as technology.
Three major factors created a situation where trench warfare could flourish. First, quick fire indirect artillery, secondly the machine gun and thirdly railroads. In 1914 the majority of armies were well supplied with breach loading, quick firing recoil dampening artillery firing shrapnel shot, 'deadly to men in open field but a mere irritant to those in the trenches, the net result of the field artillery was to strengthen whichever force was on the defensive.(1)' Artillery was, and is, the main killer on the battlefield, responsible for 60-70% of all casualties throughout the wars of the 20th century.
The machine gun was not the wonder weapon that it is commonly held up to be by the general public, what it did provide though was a very economical means of generating firepower, one machine gunner could, firing at rapid rate, produce the firepower of 5 or 10 riflemen, and more accurately too. This meant that trenches didn't need to be held in strength, and also allowed for attacking forces to be reduced in strength and disperse without a loss of firepower, where previously, with rifle armed troops, the only way to increase firepower was to thicken the firing line. Effectively, this released a large number of men that could be concentrated out of range of artillery fire, and this is where the railroads comes in.
Advancing troops, under fire from artillery and machine guns, move incredibly slowly, about 1 mile and hour or so. Additionally, reports of a breakthrough are equally slow- telephone lines get shot away by artillery, runners are killed and radios are too heavy, unreliable and unsecure to be fully utilised. In contrast the enemy was able to move his counterattack forces much faster- 40, 50, 60 miles per hour thanks to the combination of the telephone and the railroad. This speed of reaction resulted in a period of warfare where the defender was able to react with far greater speed and accuracy to the events of the war. 'What needs to be emphasised...is that no one solved the problem of converting a break-in into a breakthrough because all the technical means to do so were never available...the only arm of exploitation remained the cavalry'(2) To break the deadlock would require the creation of a effective mobile arm.
So how were these issues overcome? well first, you must create a efficient internal combustion engine. This allowed the creation of more powerful and longer ranged aircraft, and reliable armoured fighting vehicles such as tanks, armoured personnel carriers and self propelled artillery, which can protect and support vulnerable infantry as they attack machine gun positions and repeal counter-attacks. Radios allowed for commanders to ride far forwards with their troops, exploiting opportunities as they presented themselves instead of being tied to the telephone system, also allowing them to react quicker to events than the enemy was able to perceive them. Aircraft allowed for deep interdiction, destroying enemy transport systems and, in combination with paratroopers, slowed the speed of enemy reinforcements through the seizing of key terrain and constant air attack degrading the speed and capability of the enemy's response to your actions. All of this adds together to create a truly effective mobile arm that was deeply lacking during the First World War, and allowed generals twenty years later to effectively fight 'the deep battle.'
This system of warfare is popularly know as blitzkrieg, 'a combination of the tank, radio communications, and air power in the ancient maxims of offensive action, speed in decisions and the concentration of resources' (3)
(1)English, J.A. and Gudmundsson, B.I., On Infantry, (Westport, Praeger, 1994),p16
(2)Beckett, I.F.W., The Great War, (Harlow, Pearson Education Ltd., 2007),p 235
(3)Bidwell S., and Graham D., Fire-Power (Barnsley, Pen and Sword Books ltd., 1982)p205
Off the top of my head, I can think of several reasons.
Hitler utilized the new strategy of blitzkrieg (German: "lightning war"), which involved the usage of concentrated mobile armored units (tanks) and infantry backed by close-air support. Hitler also took advantage of the exciting new concept of paratroopers. These troops could be dropped behind enemy lines to capture and defend bridges. They were used in the Netherlands, which negated its usual defensive strategy of flooding the lowlands. This style of warfare allowed the German military to simultaneously invade Belgium, Luxembourg, the Netherlands, and France on May 10, 1941. Luxembourg was occupied the same day, the Dutch army surrendered on May 15th, and Belgium surrendered on May 28th.
During the Interwar Period, the French created the heavily fortified Maginot Line near the borders with Switzerland and Germany and concentrated most of their forces there (/u/elos_ has pointed out that French forces were not concentrated at the Maginot Line, but instead were deployed within Belgium). The problem was they anticipated a conflict using the same tactics from World War I (side note: their tank designs heavily reflect this, as they were essentially slow-moving, armored machine guns). The German forces also completely bypassed the Line, moving instead through the Ardennes, which the French military leadership thought improbable and so did not relocate their forces. Following a string of German victories, the German army entered Paris on June 14th.
Because of the rapidity of Germany's tactics, the Allied armies were unable to effectively fight back long enough for trench warfare to develop. But even if they were able to hold out, the improvements in tank and air technologies would not have allowed trench warfare to set in.
Tanks didn't make an appearance on the front in World War I until the war was nearly over, and even then they allowed armies to overrun enemy trenches. They were slow and heavily armored. I think a soldier could walk as fast as a World War I tank, but I might be wrong. They were also prone to breaking down. But all of these problems would be rectified during the Interwar Period. The Tiger tank, for example, was capable of sustaining speeds of almost 30 miles per hour.
Planes also firmly established their role of close-air support in the end of World War I. Fighters were efficient at strafing trenches and supply lines. Plane technology also underwent a huge transformation after World War I, mainly improving upon these basic principles.
EDIT: If those downvoting me could explain what I've said that isn't accurate, I would really appreciate it so that I can edit accordingly.