I'm interested in roads and transportation, so whenever I read history I look for these things. WWII history is very accessible, so that's where I'm most well read. I'm struck by the contrast between Operation Market Garden ("a bridge too far") and the Japanese Invasion of Singapore (who needs roads when you've got bicycle infantry?). Sometimes it sounds as though there are a very finite number of invasion routes that all parties know about, but other times the situation seems more wide open.
So, what are some examples of invasions where the roads/transportation network made a significant impact?
It's not a road, but the choice of invading Normandy over other places on the French coast was somewhat unusual. The closest place in France to the English coast is Calais, and indeed, Allied intelligence did their best to mislead the Germans into thinking the invasion would land at Calais.
In May 1940, the French army advanced into Belgium. Their best trained and equipped units were supposed to take up positions along the Dyle river, east of Brussels. They did not think the German army would make their major thrust through the Ardennes forest, because of the limited road network in that sparsely populated hilly region of south eastern Belgium. The Belgian army only deployed two of their 18 divisions in the Ardennes. "They did not fight well, being more intent on getting away from the Germans than on delaying them. The Belgian demolitions were carried out hastily, inefficiently and without covering fire." The French Ninth Army did no better. Their reconaissance units were roughly handled and fell back in disorder. It wasn't until May 13th, that the French realized the bulk of the German army, along with most of their panzer divisions, were coming through the Ardennes. The Ninth French Army had two regular and seven reserve divisions. They broke and ran on May 13th, allowing the Germans to cross the Meuse river with little resistance.
In 1944, the Germans tried to pull this trick a second time, during the Battle of the Bulge.
Source: "The German Wars" by D J Goodspeed
The entire war in Burma was basically about cutting/defending the supply route from India into China, by which the US supplied Chaing Kai Shek's Nationalist Chinese forces. These forces tied down hundreds of thousands of Japanese troops.
Also in Burma, the Imphal-Kohima offensive and riposte of 1944 was entirely dictated by roads. This battle is the antithesis of Singapore: the British learnt to tolerate having their road communications cut, while the Japanese over-confidently abandoned the road network, and when the British did not panic and lose their supply bases, mass starvation ensued.
In Europe, the Allies in France were still being supplied over the invasion beaches by improvised 'Mulberry' harbours even at the end of 1944. Montgomery captured the massive port of Antwerp but failed to clear the harbour approaches, so the port could not be used until many months later, one of the biggest failures of his career. The Germans also showered Antwerp with V2 rockets after it was opened.
The Kokoda Track battles in 1942 were conducted for control of New Guinea, and the entire battle was on the narrow front of a single walking track that was the only north-south path on the island.
In the desert the road and railway were parallel near the coast, while inland there was unlimited opportunity to manoeuvre. So infantry units were stuck on the coast and armoured-mechanised units could range inland and try to outflank the enemy. There was so much space that as battles became confused and fluid, all sorts of units could become mixed up with one another.