What could be considered the most important battles of World War I and II?
It is important to remember that these were both massive conflicts, with hundreds of battles on multiple continents, so "most important" is going to be a matter of opinion. But in general, historians often agree on a few that were critical turning points in both wars. Here are a few that might qualify:
World War I:
Battle of the Somme - This massive battle in 1916 was important in that it demonstrated what a long, bloody and futile war it would be. The British launched this offensive and in the first day lost 60,000 men. 600,000 would die before the battle was over.
Chateau Thierry - This battle in 1918 near the end of the war represented the "last gasp" of the German forces. Once the attack was stopped, mostly by US troops, the Kaiser had to sue for peace as his economy and army began to collapse.
World War II:
Battle of Stalingrad - The turning point on the Eastern Front, the entire German 6th Army surrendered, and from that point on, Hitler's forces in the Soviet Union were in almost constant retreat. Germany never had much of a chance to win in Russia, but Stalingrad marked the beginning of their doom.
Battle of Guadalcanal - This drawn out, six month battle in the Pacific pitted Japanese and American troops that were both, at one time or another, cut off from supply. Fought at about the same time as Stalingrad, this is often considered the turning point of the the war against Imperial Japan.