Archonsod said:
The Charge of the Light Brigade is a good example to be honest. They were light cavalry (unarmoured, on horses built for speed rather than stamina). For three quarters of a mile they sustained fire from riflemen and artillery from all sides, engaged heavy cavalry and returned in the same way (still taking fire) yet lost only 350 or so horses out of around 650 (and around 250 killed or captured men). Any infantry regiment in the same position would have been utterly destroyed within seconds.
No heavy cav. You're confusing with the Charge of the
Heavy Brigade, where massively outnumbered British heavy cav defeated the Russian heavy cav. The Light Brigade was supported by the French
chasseurs d'Afrique on the way back, who neutralised the Russians on one side of them (don't remember which, and to lazy to open Cecil Woodham-Smith). But yes, despite the massive losses, the Light Brigade accomplished a mission that was suposedly impossible and which they had not actually been tasked with.
Aqtai: in this instance Wikipedia is incomplete. By the late 18th century, "Uhlans" was used generically to mean "lancers" by a number of armies. The Russians, for instance, refered to all regular lancers as Uhlans (see the Memoirs of Nadejda Durova, the only woman to serve in Russian armies until WWI and who spent almost all of her career in the Uhlans--first the Konnopolski Regiment, then the Lithuania Regiment), probably to mark their difference from the Cossacks, also lancers but not technically part of the regular army. The lance never wholly disapeared from European battlefields, although it did know a low point in the 17th century. Remember that pike warfare orientated most cavalry towards the
caracolle tactics in the late 16th, and when the Swedes reminded everyone else that cavalry was most effective in a shock charge, they used swords rather than lances. However, the lance remained the primairy weapon of the Cossacks, as well as of the Polish 'winged hussars' and a number of light cavalry units also made use of it . The Uhlans themselves were more of an Austrian than a Polish creation, indeed the Napoleonic Polish Lancers suposedly only adopted the lance as their primairy weapon after the battle of Wagram, where they (reportedly) scavenged the lances of routed Austrian Uhlans.
To answer the original question:
Lances were used primairily (in the Napoleonic times) by light cavalry. The point of the lance was that it furnished the light cavalry with an effective shock weapon without sacrificing any of their mobility. The horses of the lancers and the rider's light build, also their absence of armour, were virtually the same as for the hussars (although the lance drills would probably build up more muscle than hussar training--see Durova's Memoirs for some tidbits on the daily life of Napoleonic light cav), yet the lance enabled them to effectively break the enemy square before having to collide with bayonets, so they could then use their sabres (light cavalry sabres, not the one found in Aqtai's signature) on already disorganised infantry. The lance (or pike) also gave them an advantage in a frontal charge against opposing light cav. However, the lancers neglected some aspects of skirmishing the hussars were trained in, most notably use of the rifled carbine to haras the enemy at range. Nevertheless, both types of light cav were largely suited for the same types of reconnaissance, patrol, diversion and screening missions, although the lancers were more effective in pitched battles due to their more effective charge; consequently, they were less highly specialised in the light cavalry's support duties than the hussars as they had to devote more time to training for charging with couched lance. Note that most of the details come from Nadejda Durova and that, while her anecdotes provide real information, her purpose was not to describe in detail the tactical strengths and weaknesses of her arm, and may not be wholly accurate for armies other than Russia's.
More generally, you seem to be under some misundertsandings as to the nature of warfare in the Napoleonic era. The writing was
not on the wall for the cavalry charge and would not be until the invention of the Maxim-gun. You seem to think that infantry fire was considerably more effective than it truly was; indeed, the primairy weapon of infantry in this era was the bayonet, their secondary weapon the infantry sabre, the musket being used as a support weapon--its main strength was that the same soldiers could be both the primairy shock force and their wown ranged support, softening up the enemy with repeated musket volleys as they closed before the decisive charge. In fact, the musket was a very poor weapon, due largely to its abysmal accuracy. To fully underscore just how bad this was, I have to relate part of Jean-Roch Coignet's memoirs; during the fighting in Poland in 1807, he and other grenadiers of Napoleon's Old Guard--bear in mind that these are crack troops, the best in the world at that time--go hunting (the French army is enar starvation). They manage to creep up on a herd of deer and several hares, but, to quote the man himself, "with our standard-issue muskets [fusils de munition], loaded with balls, every shot missed", even at close range on an immobile target the size of a deer. For this very reason, most armies did not even teach their recruits how to aim the things, they were just drilled in reloading them fast and firing together in the general direction of the foe. Only volleys fired at point-blank range could inflict any serious losses.
As for the bayonet, it was a much more offensive weapon that the pike, the main reason the British at first did not want to adopt it. In the end they were forced to, since Highlanders with swords had no trouble dealing with pikemen; but that is another story. Archonsod correctly pointed out its lack of reached, compared to the pike or lance, which reduced its effectiveness in defending against a cavalry charge. Contrary to popular belief, the square defensive formations did not allow infantry to withstand a cavalry attack. Their main purpose was that, with each battalion forming a separate square, the enemy would be forced to either split his forces without being able to effectively flank any unit, or else to concentrate on only a few units, in which case he would be exposed to a crossfire, which would be just as deadly to the infantry under attack as to the attackers; but in this era of mass conscription, a few battalions of the Line were expendable. The other main strength of the square formation was that it was an adaptable tactial formation, much like the Roman
manipulum, which allowed the sqaure to manoeuvre rapidly over any terrain and rapidly react to a threat from any side. However, cavalry could, and did, break the squares, for instance at the battles of Eylau (1806), Hanau (1813), and Waterlo (1815); in the later, it took the intervention (and sacrifice) of much of Wellington's cavalry to halt the French cavalry.