Cavalry charge
British and American cavalry units also made similar cavalry charges during World War II.  (See 26th Cavalry Regiment). The last successful cavalry charge of World War II was executed during the Battle of Schoenfeld on March 1, 1945. The Polish cavalry, fighting on the Soviet side, overwhelmed the German artillery position and allowed for infantry and tanks to charge into the city. The cavalry sustained only seven dead, while 26 Polish tankmen and 124 infantrymen as well as around 500 German soldiers were killed.)
After World War II, the cavalry charge was clearly outdated and was no longer employed; this, however, did not stop modern troops from utilising horses for transport, and in countries with mounted police, similar (albeit unarmed) techniques to the cavalry charge are sometimes employed to fend off rioters and large crowds.

Twenty-first century: At the start of the war in Afghanistan by United States forces, there was a cavalry charge by a unit of Green Berets led by Captain Mark Nutsch, and their use of horses in the charge was made into a Hollywood movie, 12 Strong. Across from the site of the former World Trade Center (1973–2001) there is a monument to the 'horse soldiers' who took part in that daring cavalry charge.

Age of firearms: In the age of firearms, the basic parameters are speed of advance against rate (or effectiveness) of fire. If the attackers advance at a more rapid rate than the defenders can kill or disable them then the attackers will reach the defenders (though not necessarily without being greatly weakened in numbers).  There are many modifiers to this simple comparison – timing, covering fire, organization, formation and terrain, among others. A failed charge may leave the would-be attackers vulnerable to a counter-charge.
There has been a constant rise in an army's rate of fire for the last 700 years or so, but while massed charges have been successfully broken they have also been victorious. It is only since the mid-19th century that straight charges have become less successful, especially since the introduction of the repeating rifles, machine guns, and breech-loading artillery. They are often still useful on a far smaller scale in confined areas where the enemy's firepower cannot be brought to bear. Bayonet charges are still seen in the early 20th century, but are often limited to use against adversaries with inferior firepowers, when ammunition supply is scarce, or simply as a form of suicide attack to inflict fear on the enemy.
In modern times, melee charges are practically extinct outside of riot control and street fighting, with a few exceptions such as the bayonet charge at the Battle of Danny Boy, but military charging tactics mainly take place with armored fighting vehicles such as tanks, infantry fighting vehicles, and armored cars. These ground combat vehicles can either advance directly with marching fire, or transport infantry attackers quickly into proximity with the target position in order to assault and capture it. Air assaults are also a frequently used tactic to insert special operation raids against high-value targets.

Notable charges: Battle of the Golden Spurs (July 11, 1302): The French cavalry, consisting of many nobles, was defeated in battle by heavily armed Flemish militiamen on foot. The cavalry charge was cited to be rash and premature with the battlefield's many ditches and marshes blamed for the loss, and at a few points on the Flemish line the French horsemen did manage to break through before being surrounded and annihilated. However it also demonstrated that well-disciplined and heavily armed infantry could defeat cavalry charges, ending the perception that heavy cavalry was practically invincible against infantry. The Battle of the Golden Spurs had been seen as the first example of the gradual "Infantry Revolution"  in Medieval warfare across Europe during the 14th century.

Charge of the Light Brigade (October 25, 1854) at the Battle of Balaclava in the Crimean War. Due to faulty orders a tiny force of 670 British light cavalrymen charged an enemy force many times their size. They succeeded in breaking through as well as disengaging, but suffered extremely heavy casualties and achieved no important objectives. Extensively memorialised and the subject of several literary and cinematographic works.
Pickett's Charge (July 3, 1863) at the Battle of Gettysburg in the American Civil War. A mass infantry assault on the Union lines repulsed with substantial loss. Pickett's Charge has become one of the central symbols of the literary and cultural movement known as the Lost Cause.
Battle of Mars-la-Tour (August 16, 1870): "Von Bredow's Death Ride". Prussian heavy cavalry brigade overrun French infantry and artillery to reinforce left flank of Prussian Army, at the cost of half the brigade.  One of the few notable examples of successful cavalry charges after the introduction of modern firearms. Its success won it renown among military historians, which created a myth to the effect that for some decades 'Bredow's achievement was the norm', that cavalry could still play a decisive role in battle in a modern war between equally equipped forces, and so cavalry units continued to be part of the armed forces of major European powers for the next half century.

See also: Banzai charge
Human wave attack
Bayonet charge
Highland charge

References: 
Barker, Juliet (2009). Conquest: The English Kingdom of France (PDF). London: Little, Brown. ISBN 978-1-4087-0083-9. Archived from the original (PDF) on 2018-06-12.