Pretty much every country used a whole bunch of calibres in WW2. The British Army alone, off the top of my head, had small arms in 9mm, .45ACP, .303, .30-06, 7.92 (Yes, the German calibre, standard in British tanks), .50 BMG, .50 Vickers, direct fire in 2pr, 6pr, 17pr, 77mm, 37mm, 75mm, 3", 76mm, 40mm, 3.7", plus 4.2", 25pr, and assorted other artillery and mortar calibres. Obviously this array led to problems with solutions being required. For example, the 76mm tanks were generally all sent to Italy so as to reduce the supply complexity.

The German variety was partially caused by necessity, such as the capture of enemy weapons. Sometimes they had to rechamber in order to use German munitions, but some other times, such as in the case of the Soviet 76.2mm, they captured enough ammunition that it was worthwhile to simply use the weapons in official service. eg Marder SPATG.

The other reason is simply the development of technology. The 37mm and 50mm of he beginning of the war just weren't cutting it by the end of the war. New, larger calibres were by necessity added.