Just have to point out that the Spitfire MK I was not a jet aircraft, though it certainly did see a lot of service in the war. The Me-262 was the only jet fighter to really see much service and it was so late in the war that it had almost no effect on any tactics or certainly on the outcome.
One of the technologies that was couple with an idea was that of strategic bombing like many have mentioned. But what isn't mentioned as often is the way that it put huge numbers of civilians in harm's way unlike they had been in any previous war.
We fire-bombed cities in Germany and in Japan killing literally millions of "innocent" civilians. We did this in a calculated way, even going so far as to see how much of a city we could burn with the least amount of ordinance.
This was thought of as a legitimate response to the war and one that would shorten the war though it has been up for debate since then. German war production increased until nearly the end of 1944 despite incredibly heavy bombing.
I would say that advances in war fighting was one of the most evident aspects of the Second World War. The ability to not have to get excessively close to the target in killing them is one way in which technology made war more of a distant experience. As mentioned, use of bombing campaigns from the air was one way this was possible. The notion of using precision in fighting from a distance with snipers was another advance in the technological and warfighting mindset that presented itself in the Second World War. Another significant technological advance was seen at the end of it with the use of a weapon of mass destruction. The dropping of the atomic bomb significantly changed how future wars would be fought. This helped to enhance the idea that war could be fought on massive scale from a distance, while exacting the obliteration of the opponent.
Another bit of technology that was developed during World War 2 was the Norden bomb sight. With a basic computer measuring speed, altitude, and wind-speed, it was described as being able to drop a bomb in a pickle barrel. (not true). However, it was the most accurate bomb sight during the war. This resulted in the US Army Airforce taking over the deadly assignment of bombing European targets during the day (and suffering enormous casualties as a result), while the British Air Force bombed less accurately at night.
As you can see by the many and varied answers here on World War II technology, there were a lot of innovations that changed the battlefield in World War II. I'm going to add to the mix.
Napalm was invented in 1942, and involves a mixture of powdered chemicals and gasoline that allows gasoline to burn much more slowly and to stick to surfaces it burned. Ugly, ugly, stuff, and it was actually more destructive in Japan than the atomic bombs. Remember, one of the reasons why the US chose Hiroshima and Nagasaki to bomb was because they were two of the only cities left. Napalm had burned the rest, including Tokyo.
The tank was perfected and mastered in warfare by two countries, Germany and the Soviet Union. Instead of the dangerous, primitive tanks of World War I, these were light, fast, and packed a wallop of firepower. The German Panther, Tiger and Mark IV tanks were one of the best of the war. The Soviet T-34 was the best of the war. The American Sherman was just OK, but we made so many of them we just overwhelmed the enemy.
Radar and sonar were very important in many battles that were fought during World War II. In addition, jet fighters were very popular. Some examples of these jet fighters were the Spitfire Mark 1 and the Gloster Meteor. Glide bomb weapons were also used.
The Manhattan Project was the codename that was used in the development of the first atomic bomb. It had a tremendous impact on the scientific community. This was perhaps the most devastating piece of technology that was used during World War II. It was used on Nagasaki and Hiroshima in 1945.
One of the most important inventions that was implemented during World War II was radar, an acronym (first used in 1941) for RAdio Detection And Ranging. Using electromagnetic waves, the radar detection system was able to identify range, altitude, direction and/or speed of moving and fixed objects. It was used to detect aircraft, ships and motorized vehicles in addition to weather formations and ground terrain. The British were the first to use radar extensively as a defense against German air attacks. A form of radar, sonar, was used to great effect to track German U-boats.
One major way that technology affected the fighting was that it allowed the German Blitzkrieg to happen. This "lightning war" was made possible by the fact that automobiles were much more plentiful than they had been in World War I and by the development of speedy tanks and effective airplanes. All of these (combined with better communications technology) allowed the Germans to succeed dramatically in their fighting in Europe.
Another major impact came from the development of large, long-range bombers. These allowed, for example, the US to bomb Japan very vigorously, taking off from bases hundreds of miles away in the Mariana Islands.
Finally, the development of airplanes and aircraft carriers made battleships obsolete and changed the way the war was fought at sea.
Very clearly the greatest technological development during the world war II having impact on the war was the development of the nuclear weapons . This development has completely changed the concept of war for ever, in addition to helping to bring World War II to a close faster. In addition this has also provides a foundation for technology for peaceful use of nuclear power.
Another major development during the World war II was development of missiles. The development of V1 and V2 rockets by Germany were in themselves great technological achievements. In addition, the development of this technology during the World War II, has provided solid foundation for all subsequent developments in missile technology and launching of space vehicles.