NOTE: Answer will be expanded later with more examples! Stay tuned!

Short Answer: Yes. The Germans actively recruited and used large numbers of Soviets POWs and local collaborators on the Eastern Front and Western Front. German efforts to recruit troops from Western Europe and India were less successful. The Japanese organized the India National Army to fight the British, with disappointed results.

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Long Answer: Yes. The collaboration and defection going on during WWII was so extensive and complicated that this answer will take multiple parts.

The classical definition of "defection" doesn't fit many of these cases. It implies someone has betrayed their home country to throw their support to another country. "Collaboration" might be a better fit.

Generally, foreign fighters who joined the Wehrmacht or the Waffen-SS thought of themselves as fighting for their native country, for fascism, against communism, or simply for personal survival. By and large, they didn't necessarily have any strong loyalty to Germany itself, even if they agreed with German war aims. Some were pro-fascist. Some were out and out racists. Some were anti-communist or anti-Soviet.

Other men, especially Soviet POWs, saw joining up as a ticket away from starvation in a POW camp. Still others, like many Ukrainians, saw fighting for the Germans as a way to achieve their own nationalist ambitions. By the same token, the volunteers of the Indian National Army weren't really pro-Japanese, they simply saw fighting alongside the Japanese as a vehicle for Indian independence.

Collaboration took place on a massive scale during WWII, particularly in the case of Germany. Nearly half of the nearly one million who served in the Waffen-SS were foreign-born. All in all, nearly two million foreigners served with the Wehrmacht and the Waffen-SS. Some of those foreigners were Volksdeutsche (ethic Germans living outside Germany) who volunteered or were drafted, but Nazi Germany also enlisted everyone from "Cossacks" to Norwegians to Ukrainians

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Part I: Wehrmacht Collaborators on the Eastern Front

The German armed forces used over a million former Soviet POWs. Between the Wehrmacht and the Waffen-SS, the Germans took on 1.6 million Soviet citizens (civilains and ex-POWs) as military collaborators. All in all, around 6% of Soviet POWs chose to (or were forced to)join the German forces.

Where did these collaborators come from?

1. Ex-POWs
2. Local volunteers
3. Defectors - Mark Edele says that 117,000 Soviet citizens willingly crossed German lines to defect.

All in all, ordinary Soviet citizens and POWs did what many people in Occupied Europe did. A few resisted. A few collaborated. Most didn't really chose sides and just tried to survive.

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So why did so many Soviets join the Germans? In Stalin’s Defectors, Mark Edele looks at the interrogation reports of 334 defectors made by a German infantry division, as well as diaries and memoirs. From this, he identified four motivations for Soviet collaborators:

1. Survivalism - Many collaborators were trying to escape brutal conditions on German POW camps. During the war, nearly 3.5 million men or nearly half of all Soviet POWs, died in German camps from starvation, disease, execution, and even human experimentation. To take just one example, of the 100,000 Turkestani soldiers captured in 1941, only around 6,000 were still alive by Spring 1942. "Volunteering" for the German armed forces offered some men hope for survival.
2. Defeatism - The spectacular defeats of 1941 and 1942 had badly-demoralized many Red Army POWs. By going over to the Germans, they were throwing their lot in with the (at the time) winning side.
3. Political disaffection - Of the 334 defectors, 34% were motivated by political dissatisfaction with the Soviet system.
4. Active anti-Stalinism - This was a rare motivation. Stalin's cult of personality was hard to shake, even for turncoats. Only 1.2% of the 344 defectors were driven by anti-Stalinism.

Beevor adds that many were out-and-out tricked with hollow promises.

[They] were induced, through promises [that they would be sent home to their families, instead] they found themselves in German uniforms being trained by German officers.

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