Clearly Japan was the most powerful ally of Germany, although its contribution to Germany's fortunes was dubious at best. This was for at least three reasons:
(1) Most fatally, it drew Germany into war with America (Churchill on hearing Hitler's declaration of war on America: "Oh, so we won after all").
(2) As has already been said, Japan's failure to threaten Siberia allowed Russia to withdraw key units from there to the defence of Moscow - arguably as important a turning point as Stalingrad. (IIRC, Moscow knew Japan's - lack of - intentions from a spy in Japan).
(3) The US pursued a "Germany first" policy, limiting the diversionary effect of the Pacific war on the European theatre.
Nonetheless, Japan did inflict major defeats on the allies (e.g. Singapore was regarded as the worst defeat in British military history) and tied up large amounts of allied resources.
Italy was the other major ally of Germany, but was arguably a liability.
(1) It made no real contribution to the conquest of France, coming in late and getting bogged down in the southeast.
(2) Its humiliations in North Africa sucked Germany into a peripheral theatre, ultimately leading to the surrender of a large German army (IIRC a quarter of a million men) in Tunisia.
3) It got bogged down in Albania and forced the Germans into a Balkan campaign that delayed Barbarossa, perhaps fatally, and then at Crete dissuaded Germany from ever again using paratroops in large deployments.
The loss of Italian forces in 1943 did not appear to significantly hamper the Germans, who slowed Allied progress up Italy to a crawl.
Seriously, it is hard to think of good examples of the successes of Axis cooperation. I suppose Germany's European allies - Finns, Italians, Romanians, Hungarians etc - helped maintain the line in the vast Eastern front. And, as Kraxis has said, the Italians manned much of the North African front. But most Axis successes were almost purely German or Japanese achievements - even in the desert, it was two or three German divisions that made most of the breakthroughs.
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