In many cases a successful charge relied on the targeted infantry having some degree of 'discipline', precisely because the knights' effectiveness increases against a uniform, static enemy. I can comment on the crusade era in relation to this.

Frankish knights used lances to project and focus the combined weight of their own armour and mount ahead of themselves and onto the enemy - in this way they delivered a blow to their target before they impacted with it themselves. The forward, inertial momentum of this impact, combined with the individual skill of the knight, would be devastating to any lightly and/or moderately armoured opposition.

The charge subsequently acquired a psychological element, in which it was expected and feared by a knight's opposition, particularly by those cultures and nations which did not deploy it in warfare themselves. This terrorising quality may have been useful in its early usage against the Middle East's native armies, but also meant that it was soon planned for and defended against.

During the crusades, a 'well-prepared and disciplined infantry' learned that evading the charge was the only completely effective defense against it. As I alluded to earlier, standing up to the charge was not a prudent strategy for any but the most heavily armoured troops, especially in this theatre.

[the charge] depended for its success on impact with an enemy, who, in resisting, would be shattered by its weight. If the enemy, like the Turks, was able to remove himself from its path, then the Franks, their formation loosening as they advanced, were vulnerable to counter-attack. (Smail, 1956)

Essentially, a charge was a one-off in most cases. If it found its target then the successful knights would often carry the field and the day. However, the common inability of a Medieval commander to reliably recall and reform his detachment of knights made any second attempts unlikely.

For example, in 1167 at the battle of Al Babein the charge was misdirected, failed to make a significant impact and so the day was fought to an inconclusive draw. Muslim armies, which often enjoyed superior levels of tactical maneuverability, could 'open' their lines to evade a Frankish charge, only to 'close' again to trap any foot-soldiers. Another tactic was to field weaker, 'less valuable' troops against the charge, thereby protecting more important troops.

By contrast, in 1191 at the battle of Arsuf the charge landed fully against valuable targets and precipitated a rout. Initially only one detachment of knights, those of the Knights Hospitaller, charged the enemy. Recognising the need for cohesion, the army's commander, Richard I of England, launched the entire charge in support. In finding its target the charge carried this particular engagement. This is not to suggest that nothing but the charge mattered in the outcome of a battle, but it could give one combatant a considerable advantage over the other.

Other people will be able to give you details on differing eras and theatres, hopefully this helped.

See: Crusading Warfare, 1097-1193 R. C. Smail (1956)

Edit: Formatting.

They need to look for a weakness in the line and be prepared to exploit it.

Note that in the Napoleonic era there was only one recorded instance of cavalry routing a disciplined square - and that involved having a charging horse from the King's German Legion be killed mid-stride and smashing into the French square. This opened a gap which allowed the cavalry to pour into the square and rout the rest of the troops.

Charging directly against a solid line simply did not work like in The Lord of the Rings - the horses simply won't run over men without gaps; and even if the horses are somehow tricked into trying the men on the ground could still wound or kill the horses using their own weapons. But maintaining a solid line even with more disciplined troops is not an easy exercise, especially since terrain was rarely flat even ground and just a few soldiers lapsing or panicking can doom the rest.