There are a few factors for this.
One, and most notably for those aces that top the all time list, is that they very often flew until they died or were otherwise unable to continue flying. For example, the all time ace of aces, Erich Hartmann, first joined up in 1940. He was then posted to front line duty in October 1942. He flew until the end of the war, securing his final kill in early May, 1945. The Japanese, who also had a few pilots rack up a large number of kills, also often flew in such a manner. While this allowed them both to have pilots that attained extremely high numbers of kills, it also came back to bite them in the ass later in the war as more and more pilots were killed. Their ranks simply became thinned of experienced pilots to lead the less experienced ones into battle, and also to pass on their knowledge. The Allies on the other hand, especially the Brits and Americans, tended to rotate pilots back home to spread their knowledge and experience with the next round of trainees. So simply put, the Allied pilots just didn’t have a chance to rack up huge numbers.
Both the Japanese and Germans also had a technical superiority edge over their early opponents. The Germans for example, often came across obsolete Soviet aircraft manned by poorly trained pilots and poorly organized commands. The Germans also took home valuable lessons from their experience in aiding the Nationalists in the Spanish Civil War. It should also be noted that despite what you may hear about such vaunted aircraft as the P-51 supposedly being so superior to the German offerings, the Germans actually kept up pace relatively well with the Allies throughout the war in terms of fighter design. The two principle fighters of the Luftwaffe, the Bf-109 and Fw-190, were both constantly updated and improved to keep pace with fighter design improvements and more or less kept an even edge with their Allied counterparts. There was a bit of back and forth wherein one side might for a very short time attain a technical superiority over the other side, but such instances were always short lived. In any case, what it almost always came down to was pilot skill (in other words, any technical superiority would have been minimal and easily overcome by an experienced pilot fighting to his strengths and his opponents weaknesses).
Another aspect is simply how kills were tallied. The Germans had a “one pilot, one kill” system. This meant that only one pilot could claim the victory even if more than one pilot contributed to the kill. For various reasons, the more experienced pilot may be given credit for the kill. British and American pilots used a fractional system, wherein credit could be shared among pilots but the total would still equal one (so two pilots shooting down one aircraft would be awarded 0.5 of a kill, four pilots taking down an aircraft would each achieve 0.25 of a kill, etc). I will have to double check on the Soviets as it escapes me what system they used, but I’m pretty sure they, like the Japanese, awarded kills only for solo victories, and counted partial kills separately (though the Imperial Japanese Navy abandoned individual victories for those of squadron victories in I believe mid 1943). The French awarded one kill to each contributing pilot (so four pilots contributing to a kill would all receive a full credit for one kill. So you might have one downed aircraft, but four claimed kills by four different pilots). The Finns, who also have a few aces pretty high up on the list (and the highest ever non-German ace) also used the fractional system as the Brits and Americans. The Americans also, at times, counted aircraft destroyed on the ground as an aerial victory.
Another reason for German domination of the list of all time aces, with the vast majority of these coming in WWII, is that expert pilots often seemed to be clumped into the same squadrons. Part of this is simply due to the fact that expert pilots can go on to share their experience with lesser experienced pilots, who then learn from these teachings and go on to become experts themselves. Jagdgeschwader 52 for example, is the most successful fighter wing in the history of aviation, and counts the top three aces of all time as members of the unit. JG52 started off in the Battle of France and Battle of Britain, where it didn’t really stand out, but upon transfer to the Eastern Front, they started racking up kills. In the last 6 months of 1941, they racked up nearly 1000 kills to only about 50 losses. Six months later, they had racked up another 500 kills, and then in the period of a month in mid 1942 they had racked up another 500. 500 victories in a single month. All told, they claimed over 10,000 victories for a loss of roughly 750. Quite staggering really. Again, part of this is because of their technical superiority, but also experience. So as you can see, it all kind of ties together. Their technical superiority may have made survival more likely, leading to more experience, which would pay off as the Soviets came up to speed in both pilot training and equipment.
But if I had to pin it on one factor alone, it would simply be the duration of a pilot’s time on the front line. As I said before, most of the Allied pilots simply didn’t have the time to accumulate large numbers of kills.
In general, German pilots served until they were incapacitated in combat rather than the rotation into other roles like the Allies used (training, promotions to higher command, fund raising via war bond drives, etc). High sortie rates (number of missions per time period) in the early part of the war gave individuals more chances to score than their opponents. German pilots were more experienced as well, given that many of them had practiced their craft during the Spanish Civil War (where as many pilots as possible were rotated to maximize experience gained) and also during early campaigns in Poland, Norway, and France. Once the war against Russia began, the Germans faced inferior (in terms of experience and training, as well as tactics) pilots in inferior planes and were able to rack up impressive numbers against obsolete aircraft. Most (but not all) of the highest scoring German aces served for long stretches on the Eastern front.
A quick aside must be mentioned: "confirmed kills" is far from 100% scientific. Each nation had their own policies regarding how kills were awarded. Shared kills, partial kills, planes damaged, and other categories varied wildly both by nation and over time in the war. Even one "confirmed kill" could be quite different from another. For instance, a plane that was clearly damaged (with friendly witnesses) and set aflame but disappeared into a cloud bank could either be scored a kill, a probable kill, a damaged aircraft, or not counted at all if there was no gun camera footage of the incident. Any number of reasons could result in inflated kill numbers: the problematic nature of eyewitness testimony, the distorting effects of adrenaline and fear on pilots, the pressure from your superiors to get results as well as self-motivation to do your job well, and the propaganda value of claiming many destroyed aircraft. Claimed kills were often much greater than actual kills during WWII.
That said, the German aces did indeed score high numbers of kills. They were talented, experienced, and motivated pilots that flew planes that sometimes heavily outclassed their opposition--especially early in the war. The lack of rotation out of combat increased their number of sorties flown, and the length of service for some of these pilots was quite long. Their numbers may be a bit inflated, but likely no more than other pilots from other nations.
Very good answers. It is also worth pointing out that the Germans were hugely outnumbered, especially as the war dragged on. When German pilots flew up they were statistically more likely to find targets. When Allied pilots flew, there were hardly any German planes to shoot down.
Gunther Rall, an extremely successful German Ace (275 kills, virtually all against the Soviets), was [interviewed for the game Janes WWII Fighters and addresses this explicitly.] (http://www.youtube.com/watch?v=STFdRrWBW2w&t=1m0s)