Cavalry
This unit still exists in the Pakistan Army as an armored regiment.

World War II: While most armies still maintained cavalry units at the outbreak of World War II in 1939, significant mounted action was largely restricted to the Polish, Balkan, and Soviet campaigns. Rather than charge their mounts into battle, cavalry units were either used as mounted infantry (using horses to move into position and then dismounting for combat) or as reconnaissance units (especially in areas not suited to tracked or wheeled vehicles).

Polish: A popular myth is that Polish cavalry armed with lances charged German tanks during the September 1939 campaign. This arose from misreporting of a single clash on 1 September near Krojanty, when two squadrons of the Polish 18th Lancers armed with sabres scattered German infantry before being caught in the open by German armoured cars.
Two examples illustrate how the myth developed. First, because motorised vehicles were in short supply, the Poles used horses to pull anti-tank weapons into position. Second, there were a few incidents when Polish cavalry was trapped by German tanks, and attempted to fight free. However, this did not mean that the Polish army chose to attack tanks with horse cavalry. Later, on the Eastern Front, the Red Army did deploy cavalry units effectively against the Germans.

A more correct term would be "mounted infantry" instead of "cavalry", as horses were primarily used as a means of transportation, for which they were very suitable in view of the very poor road conditions in pre-war Poland. Another myth describes Polish cavalry as being armed with both sabres and lances; lances were used for peacetime ceremonial purposes only and the primary weapon of the Polish cavalryman in 1939 was a rifle. Individual equipment did include a sabre, probably because of well-established tradition, and in the case of a melee combat this secondary weapon would probably be more effective than a rifle and bayonet. Moreover, the Polish cavalry brigade order of battle in 1939 included, apart from the mounted soldiers themselves, light and heavy machine guns (wheeled), the Anti-tank rifle, model 35, anti-aircraft weapons, anti tank artillery such as the Bofors 37 mm, also light and scout tanks, etc. The last cavalry vs. cavalry mutual charge in Europe took place in Poland during the Battle of Krasnobród, when Polish and German cavalry units clashed with each other.
The last classical cavalry charge of the war took place on March 1, 1945, during the Battle of Schoenfeld by the 1st "Warsaw" Independent Cavalry Brigade. Infantry and tanks had been employed to little effect against the German position, both of which floundered in the open wetlands only to be dominated by infantry and antitank fire from the German fortifications on the forward slope of Hill 157, overlooking the wetlands. The Germans had not taken cavalry into consideration when fortifying their position which, combined with the "Warsaw"s swift assault, overran the German anti-tank guns and consolidated into an attack into the village itself, now supported by infantry and tanks.

Greek: The Italian invasion of Greece in October 1940 saw mounted cavalry used effectively by the Greek defenders along the mountainous frontier with Albania. Three Greek cavalry regiments (two mounted and one partially mechanized) played an important role in the Italian defeat in this difficult terrain.

Soviet: The contribution of Soviet cavalry to the development of modern military operational doctrine and its importance in defeating Nazi Germany has been eclipsed by the higher profile of tanks and airplanes. Soviet cavalry contributed significantly to the defeat of the Axis armies. They were able to provide the most mobile troops available in the early stages, when trucks and other equipment were low in quality; as well as providing cover for retreating forces.
Considering their relatively limited numbers, the Soviet cavalry played a significant role in giving Germany its first real defeats in the early stages of the war. The continuing potential of mounted troops was demonstrated during the Battle of Moscow, against Guderian and the powerful central German 9th Army. Pavel Belov was given by Stavka a mobile group including the elite 9th tank brigade, ski battalions, Katyusha rocket launcher battalion among others, the unit additionally received new weapons. This newly created group became the first to carry the Soviet counter-offensive in late November, when the general offensive began on 5 December. These mobile units often played major roles in both defensive and offensive operations.
Cavalry were amongst the first Soviet units to complete the encirclement in the Battle of Stalingrad, thus sealing the fate of the German 6th Army. Mounted Soviet forces also played a role in the encirclement of Berlin, with some Cossack cavalry units reaching the Reichstag in April 1945. Throughout the war they performed important tasks such as the capture of bridgeheads which is considered one of the hardest jobs in battle, often doing so with inferior numbers. For instance the 8th Guards Cavalry Regiment of the 2nd Guards Cavalry Division (Soviet Union), 1st Guards Cavalry Corps often fought outnumbered against elite German units.
By the final stages of the war only the Soviet Union was still fielding mounted units in substantial numbers, some in combined mechanized and horse units. The main advantage of this tactical approach was in enabling mounted infantry to keep pace with advancing tanks. Other factors favoring the retention of mounted forces included the high quality of Russian Cossacks, which provided about half of all mounted Soviet cavalry throughout the war. They excelled in warfare manoeuvers, since the lack of roads limited the effectiveness of wheeled vehicles in many parts of the Eastern Front. Another consideration was that sufficient logistic capacity was often not available to support very large motorized forces, whereas cavalry was relatively easy to maintain when detached from the main army and acting on its own initiative. The main usage of the Soviet cavalry involved infiltration through front lines with subsequent deep raids, which disorganized German supply lines. Another role was the pursuit of retreating enemy forces during major front-line operations and breakthroughs.

Hungarian: During World War II, the Royal Hungarian Army's hussars were typically only used to undertake reconnaissance tasks against Soviet forces, and then only in detachments of section or squadron strength.
The last documented hussar attack was conducted by Lieutenant Colonel Kálmán Mikecz on August 16, 1941, at Nikolaev. The hussars arriving as reinforcements, were employed to break through Russian positions ahead of German troops. The hussars equipped with swords and submachine guns broke through the Russian lines in a single attack.
An eyewitness account of the last hussar attack by Erich Kern, a German officer, was written in his memoir in 1948:

… We were again in a tough fight with the desperately defensive enemy who dug himself along a high railway embankment. We've been attacked four times already, and we've been kicked back all four times. The battalion commander swore, but the company commanders were helpless. Then, instead of the artillery support we asked for countless times, a Hungarian hussar regiment appeared on the scene. We laughed. What the hell do they want here with their graceful, elegant horses? We froze at once: these Hungarians went crazy. Cavalry Squadron approached after a cavalry squadron. The command word rang. The bronze-brown, slender riders almost grew to their saddle.
Their shining colonel of golden parolis jerked his sword. Four or five armored cars cut out of the wings, and the regiment slashed across the wide plain with flashing swords in the afternoon sun. Seydlitz attacked like this once before. Forgetting all caution, we climbed out of our covers. It was all like a great equestrian movie. The first shots rumbled, then became less frequent. With astonished eyes, in disbelief, we watched as the Soviet regiment, which had so far repulsed our attacks with desperate determination, now turned around and left its positions in panic. And the triumphant Hungarians chased the Russian in front of them and shredded them with their glittering sabers. The hussar sword, it seems, was a bit much for the nerves of Russians. Now, for once, the ancient weapon has triumphed over modern equipment ....

Italian: The last mounted sabre charge by Italian cavalry occurred on August 24, 1942, at Isbuscenski (Russia), when a squadron of the Savoia Cavalry Regiment charged the 812th Siberian Infantry Regiment. The remainder of the regiment, together with the Novara Lancers made a dismounted attack in an action that ended with the retreat of the Russians after heavy losses on both sides. The final Italian cavalry action occurred on October 17, 1942, in Poloj (now Croatia) by a squadron of the Alexandria Cavalry Regiment against a large group of Yugoslav partisans.

Other Axis Powers: Romanian, Hungarian and Italian cavalry were dispersed or disbanded following the retreat of the Axis forces from Russia. Germany still maintained some mounted (mixed with bicycles) SS and Cossack units until the last days of the War.

Finnish: Finland used mounted troops against Russian forces effectively in forested terrain during the Continuation War. The last Finnish cavalry unit was not disbanded until 1947.

American: The U.S.