According to wikipedia the Germans had an ungodly amount of pilots with an insane number of kills. I have a feeling that they basically were just teeing off on inferior Soviet pilots and aircraft, but is there any more to it?
Numerous German pilots had 100+ kills against the Western allies as well, (far more than the top Americans had, for example.). eg. Egon Mayer for example or Hans-Joachim Marseille. Adolf Galland is famous
The Germans had no policy to rotate pilots out after a set number of missions. This has been described as "fly till you die". They flew until they were out of action, often severely wounded or killed or captured. It handicapped the Germans in the long run, because the experience wasn't used to train new pilots and upskill them. Yet it also meant that the best German aces had opportunity after opportunity.
They were in a target rich environment and defending their homeland. Yes, there may have been an element of a turkey shoot in the east, where there were (at least initially) a large number of poorly trained Soviet soldiers with inferior equipment and tactics. . However this is not all of it; as time passed the soviets fielded better equipment, tactics and also some flyers.
The Germans were also able to go through a number of sorties a day. Many of the German aces were shot down and were able to return in short order to the battlefield (instead of being taken PoW or lost at sea)
The common German fighters including the Bf109, Fw 190 and later the Me 262, were typically competitive and sometimes cutting edge (though this varied over time and place, it was definitely true for a while in the east and at spots in the west); this definitely played a part in their survival and also in victories.
The Luftwaffe also started the war off with good tactics, logistics and operations, thanks to lessons learned from the Spanish civil war. eg 'Vatti' Moelders developed the rotte and the schwarm instead of tight V formation flying.
The German aces received recognition in terms of rewards/medals and often adulation, while some other airforces didn't as much.
I'd say the terrible state of the VVS definitely plays a part, but even before Barbarossa the Luftwaffe had a culture that catered to fighter aces. Competition between aces was encouraged from the top and Goebbels propaganda machine lavished praise on Germany's high scorers. The experience and tactics set developed in the Spanish Civil War has already been mentioned in this thread, but another aspect that assisted aces was the a hunter-wingman system, where every four plane schwarm was split into pairs, with the more experienced 'Jager' watched over by his 'Katschmarek'. As well, best pilots tended to have their pick of wingman, amplifying the trend.
Source: Stephen Bungay, The Most Dangerous Enemy: a History of the Battle of Britain, 2001