As to the depression, it is apparent that neither Hitler nor FDR can take 100% of the credit for ending the depression but importantly their policies of public spending turned things around and there was finally growth and development again. Similar things happened throughout the world as economies slowly regained strength. In fact, although unemployment was still critically high by the outbreak of war, there was more money going around as well as a desire for resources.
The idea of war in 1931 was impossible, countries could barely support themselves. But by 1939 they had money, wanted resources and had a lot of unemployed men to fill up the ranks of large armies. I don't think it was the war that ended the depression, at least it couldn't do it by itself but it certainly marked the end.
But we have to realise at the moment we are not in a depression, we are in a recession.
During the last big recession, the 70's oil Crisis, Western countries became a lot less involved, US pulled out of Vietnam, and coincided with Détente and a warming of Cold War relations. There was lots of internal political turmoil in various countries but inter-country conflicts were less than in the 50's and 60's.
But that is just a general rule, as economic troubles lead to political troubles that weaken the government and will inhibit them going to war, but the same thing may be exploited by countries that seize this indecision and uncertainty as a time to strike like possibly the Yom Kippur War.