There were large pockets of organized resistance in 1940, but they surrendered when their governments did. For the few governments who kept fighting, they had plenty of holdouts. The Axis powers did not surrender until 1945 when almost completely overrun, and they ordered their armies to keep fighting to the last.
Many Allied powers surrendered, or were forced into exile, in or before 1941 and thus their militaries on the mainland were ordered to stopped fighting. In rough order: Austria, Czechoslovakia, Poland, Denmark, Norway, Luxembourg, Netherlands, Belgium, France, Yugoslavia and Greece (with Latvia, Lithuania and Estonia being occupied by the Soviets). In contrast most European Axis powers did not surrender until spring 1945 and were fanatically ordered to keep fighting.
What would have become pockets of resistance in 1940 were simply surrendered. The rest of the country was conquered and there was no point to the fighting. Many of the "Allies" in 1940 were actually neutral, so there was no joint plan of retreat when one country was overrun. Governments were terrified of the German threat to level their cities with bombers (a novel concept in 1940) if they resisted (as the Bombing Of Rotterdam illustrated) and were more likely to capitulate than fight on. Paris was declared an Open City rather than suffer a battle. Nobody realized how bad Nazi occupation would be.
The great German innovation in warfare in 1940 was the Blitzkrieg, the Lightning War, where the situation changes too fast for the enemy to react effectively. This also counts for governments, watching their armies get surrounded, ordering defense lines prepared not realizing they have already been breached, having their cities and supply lines bombed. In 1940, the Allied armies were not prepared for this and Germany seemed unstoppable. France, Belgium and Netherlands still held considerable territory and arms, and they had plans to form national redoubts in small corners of their countries, but they were losing so fast surrender seemed the only option.
However, some of these had extensive colonial assets and armies which continued to fight on, France, Netherlands and Belgium in particular had extensive Pacific and African colonies. I would count these as "holdouts". Most of their Far East colonies were later taken by the Japanese.
Many soldiers in occupied countries joined resistance groups, particularly in Greece, Norway and Yugoslavia (a lot of rugged terrain to hide in). Governments-in-exile were continuously trying to bring these groups under their control to avoid facing an armed coup when they returned.
By 1941, most of the European Allies had been knocked out of the war, so there were no organized hold outs. In contrast, the Allies which were still fighting (US, UK and the Soviets) did have holdouts.
After the Japanese attacked Pearl Harbor and left the US Navy unable to support the US Pacific islands, the US army continued to fight a doomed battle. The Battle Of The Philippines lasted six months and Corregidor held out until May 1942. Wake Island held out for two weeks after Pearl Harbor.
The UK had whole armies in North Africa and the Middle East effectively cut off by the German conquest of France, the hostility of the French North African governments, and the threat of Italian naval and air power. They kept fighting. On a smaller scale, Malta and Tobruk held out under siege. Neither could be bypassed nor surrendered, they were vital for supplies. Fighting also continued in India, Burma and East Africa.
The Eastern Front featured huge armies being surrounded and swallowed up first by the Germans, later by the Soviets. There were also surrounded holdouts. Most famously Leningrad was besieged for over 2 years. Sevastopol held out for eight months after the rest of Crimea was conquered and the front had moved far on. Stalingrad held out, and then it was the Sixth Army's turn.
Cut off by neutral neighbors and receiving no support from the Allies, the whole of Finland during the Winter War could be said to be "holding out" against the Soviets. Within that war, whole Soviet divisions were trapped deep in the Finnish wilderness but rather than surrender they would hold out for weeks vexing the greatly overstretched Finns who desperately needed the men elsewhere.
In contrast to the Allies' flexible ideas about reconquest, Hitler (but not his generals) had an increasingly mad notion of never giving up an inch of captured soil. This is a terrible strategy and which left armies in bad positions and many good soldiers and material trapped behind enemy lines. Many armies which could have retreated to fight another day were left surrounded to "fight to the last bullet". Unsupplied armies rapidly become immobile due to lack of fuel and spare parts and are no longer a threat: they simply can't move.
During the reconquest of Europe the Allies had a clear strategy: get to Berlin before the other guy does. Anything that didn't help getting to Berlin was bypassed. To bother with a siege it had to be either in the way, a danger to the rear, or helping with the supply problem.
While we usually think of the Channel Ports as being the classic example of an army bypassed, they were initially of great importance to the Allies and the First Canadian Army was tasked with taking them. They were not considered a threat: the garrison troops being of low quality and lacking mobility; the Germany navy hardly existed as a fighting force, what was left was busy shelling the Soviets in the Baltic; and the German Air Force was desperately defending Germany from Allied bombing. The ports were badly needed for supply, so they would be taken quickly in September 1944.
In contrast, the Atlantic Coast was ignored: west was the other way from Berlin, the ports were too far away from the front to help their supply situation, and the U-Boat threat was defanged. It is only here (with the exception of Dunkirk) that we see Hitler's declared fortress cities hold out.
Most of the declared German fortress cities were taken, in part because it was a political rather than military decision to declare a city a fortress. Only a handful held out to the end and most because they were simply ignored.