How far can Germany war plane fly without refueling in WW2?

Answer 1

Dennis is quite correct in his numbers.
However, the Germans never invested heavily in long range heavy bombers (although they called them that). They invested heavily in small Stukas and medium bombers (which better suited their Blitzkreig offenses).
The heaviest bomber was the Junkers Ju 88 with a range of 2,108 km (1,310 mi). Which meant it could only last over British targets in the Battle of Britain for a relatively short time.

Answer 2

The German Messerschmitt Bf 110 heavy fighter had a combat range of about 1500 miles.

The Heinkel He 177 Recon/Heavy Bomber had a combat radius of about 950 miles and a ferry range of 3200 miles.