Going back to the original topic, it's very interesting. I've been thinking about it before for some time. Unfortunately, I think the answer is probably the BF 109. I'll explain why. I see WW2 as mainly three theatres, the Western, Eastern and Pacific. Of these three, the Eastern front was by far the biggest. Aircraft such as the Hellcat may have decimated the Japanese carrier air force and the TBF/M sank a staggering amount of Japanese shipping, but their impact was really only limited to one of the 2 smaller fronts.
Also, while the big, famous battles like Midway are important, all the hundreds of smaller battles and skirmishes that slowly wore down the enemy are equally or more important and directly impacted the big battles. Stalingrad is a prime example; it's where the attrition the Germans had suffered finally caught up with them and no amount of tactical superiority could protect them against the vast resources of the Soviet Union.
With that in mind, here are my picks:
Spitfire
West:
- Made a major contribution to the Battle of Britain. More kills per aircraft and lower loss rate than the Hurricane.
- Played a major role in the defense of Malta and establishing air superiority over North Africa. This eventually led to the invasion of Italy.
- Ground the Luftwaffe in Northern France down for years, despite a slight pause when the FW 190 appeared. Continued to constantly bleed the Luftwaffe with the mark IX and later marks from mid 1942 onwards.
East:
- The Mark V was used by the Russians, but was not very well liked; it was good at high altitudes, where not much combat took place.
Pacific:
- Played an important role in the defense of Darwin and some other local theatres.
B 24 Liberator
West:
- Attacked the Romanian oilfields and contributed to the CBO over Germany from 1944. This would eventually lead to Germany's chronic lack of resources and final collapse.
- Helped close the mid-Atlantic gap.
Pacific:
- Plays a significant role in bombing Japanese bases due to range.
P 40
West:
- Played an important role in North Africa. Less so after D-day.
East:
- The Russians liked their ruggedness and low altitude performance. Second only to the P39 in popularity for lend-lease aircraft.
Pacific:
- Important in the early years in the Pacific, especially over China and New Guinea
Yak fighter family
East:
- The Yak 1 was about the only decent fighter the Soviets had at the start of the invasion (e.g. it wouldn't rip the wings off if you farted)
- The Yak 9 was the newest and best Soviet fighter over Stalingrad and was produced in larger numbers than any other Soviet fighter.
- From mid 1944, the Yak 3 was the best low-altitude dogfighter in the world; German fighters would do all they could to avoid it rather than risking a dogfight.
Il 2 Sturmovik
East:
- Not very accurate, but built in such vast numbers they destroyed an enormous amount of German tanks and equipment. It didn't hurt that German troops were scared to death of them.
- Forced the Luftwaffe to expend an enormous amount of resources to try and bring the endless waves down. So tough that the Germans called them "the concrete aeroplane".
BF 109
West:
- The Germans were smart and lucky when they conquered France. Without the 109 covering the Stuka's and bombers, the outcome could have been very different.
- The only aircraft to do any serious damage to fighter command over Britain.
- Inflicted horrific losses on the Mighty 8th during 1943. Remained a threat right up until the end.
- Was present in every major war Germany fought in the West and was pivotal in Scandinavia, the Balkans, North Africa, Greece etc.
East:
- Absolutely dominated the skies over Russia right up until 1943. It's doubtful the Germans would have gotten anywhere near Moscow without it.
- History's greatest aces all flew the 109. Their kills range in the hundreds and there were many of them. The best Western allied aces scored below 50.
Less relevant than people think: B 29
- Based on discussions among the Japanese high command during the final days of the war, there is significant evidence that Japan surrendered largely because the Soviet Union entered the war. For months, B 29's had been firebombing Japanese cities, causing far more civilian deaths than the 2 atom bombs would. As many people have pointed out, civilian deaths seem to have had almost no impact on the will to fight in any country throughout the war. By contrast, the Soviets handed the Japanese army their ass in Manchuria within a matter of days. With supplies now cut off from all angles, the Japanese warlords shat their pants.
So hence my conclusion. Much as I'd like it to be an Allied aircraft, without the BF 109, there my not have been much of a war to begin with. It was present and decisive in every major battle the Germans fought. Superior aircraft did appear, but it remained at least competitive and influential from 1939 all the way to 1945.