I am by no means an expert, but here's one possible scenario. Essentially, if Operation Barbarossa and Pearl Harbor had gone differently, the Axis could've won.
Early in WWII (pre 1941), Britain was the greatest adversary Germany faced. At this point, Germany held Poland, Sweden, the Netherlands, Belgium, and France. It was also allied with Italy. Its hard to imagine how powerful Germany was. Just looking at a map of Europe, you can only imagine how massive Germany was.
Hitler believed (and was probably correct) in thinking that the only reason Britain still held out against Germany was because of possible Soviet or American intervention. He left America to the Japanese, and focused personally on keeping the Soviets out of the war.
In June of 1941, Operation Barbarossa is launched. This event is the largest invasion in the history of humanity, and results in nearly five million military causalities. Hitler had always wanted to destroy the Soviet Union, and by the summer of 1940, facing a materials shortage and potential conflict over the Balkans, it became his only option.
While Stalin knew that Hitler was planning to invade, he didn't expect it to happen so suddenly. In its early stages, the invasion was a huge success. It soon turned into a disaster. Hitler had deeply underestimated how quickly the Soviet Union could recruit soldiers. On average, half a million men were drafted every month, something that Hitler had never even considered possible.
Furthermore, it was assumed that the Red Army would completely collapse, in part due to Stalin's Officers Purge. Because of this, the Germans weren't prepared logistically for a long war. Not only that, but what little supplies they didn't have often didn't reach the troops, due to poor weather and unexpected partisan resistance.
Operation Barbarossa came to its end at the Battle of Moscow. Beforehand, despite all of its failings, it still had a chance. However, poor weather forced the 3rd Panzer Army, which had come within 90 miles of Moscow, to cease its advance. This gave the Soviets time to raise eleven new armies, bringing 1,000 tanks and 1,000 aircraft to the Western front.
If the weather had been better, and if the 3rd Panzer Army had been able to seize Moscow, this may have caused the complete collapse of the Soviet Union. These are big ifs, but they were still serious possibilities that were considered by both sides. This would've resulted in...
Countless German soldiers would've been demobilized following the success of the campaign. This would've solved Germany's labor shortage.
Ukraine would've solved the agricultural shortage, and the Baku Oilfields would've solved the oil shortage.
The Germans would be far less economically strained, and would've been allowed to concentrate on Britain. History would have been so radically different that's its hard to imagine what would've happened.
For starters, there would be no D-Day. D-Day had only been allowed to happen by three years of Soviet pressure, drawing soldiers away from France. Britain might surrender, as Hitler hoped. Pearl Harbor might not have happened, because the Japanese might not have needed the resources (instead, they could rely on Germany). The US might have never gotten involved.
This is only one of many possibilities, and like I've said, I'm not an expert.
Source: Why The Allies Won - Dr Richard Overy - ISBN-10: 1845950658.
This might be a bit "what if"; I'll leave it to the mods to decide.
The best chances for Germany to win were at the beginning before the Allies were able to build up their armed forces. Having blown that chance, allied industrial might, and Hitler's propensities for making disastrous decisions, doomed the German efforts.
Overy argues that Hitler's image of sheer unpleasant nastiness was very significant in mobilising the Allies. It made it easier for the Allies to sell the war as a narrative of good against evil.
Japan lost arguably its only change of winning by attacking the US at Pearl Harbour instead of the Soviet Union.
This is best asked in /r/HistoricalWhatIf, as we don't allow such speculation here.