Mounted Combat

The Cool Horse has always been useful in fiction for heroes in all ages of literature, but fictional representations of the blessed steeds are often quite different to reality. In mounted stage combat, the horses are perfectly happy to just stand still next to each other while their riders (pretend to) hack away at each other, something of a contrast to the heat of battle. The riders/fighters have to simultaneously guide the horses into moving around each other so as to make it look like something's happening. Mounted combat is shown in varying degrees of realism, like in the rest of fiction. For help deciding how realistic a scene is, consulting the Useful Notes section on mounted combat may be helpful.

In Video Games, horsemen tend to be very expensive, fast moving and powerful units which are excellent if you can afford them... but also tend to come with one cheap opposing unit which can stop them.

Anime and Manga

Shigure in Kenichi: The Mightiest Disciple faces off against a master of Mounted Combat. She ends up trumping his horse with a motorcycle.

Film

Semi-realistic depiction in the Two Towers movie of The Lord of the Rings. On one hand, the charge out of Helms Deep at the end, with the cavalry held close together in tight formation and essentially being used to force the infantry back, before eventually getting bogged down and into trouble when the orcs numbers and discipline begin to show, is fairly accurate. On the other hand, Gandalfs relief charge would probably have ended up a) making a sad retreat after dancing around a pikeline for a few hours or b) completely butchered.
- Gandalfs charge had decidedly abnormal help in this regard however; Gandalf used the Uruk-Hais aversion to light against them. On the other hand, cavalry are also not good for charging over rough terrain; charging down a massive rocky hill like that would have risked several horses stumbling and breaking up the whole charge; horses are best suited to the plains, which, to be fair, constituted the majority of Rohan. Gandalf may simply not have had much of a choice of where to charge from.
  - It's not necessarily their aversion to light that made them do that. It was in part because they were looking straight at the sun. Try concentrating on fighting while you have a sudden bright light in your eyes.

Literature

J.R.R. Tolkien (The Lord of the Rings) and Robert Jordan (The Wheel of Time), who both have military experience and did their research, are known for using cavalry and other military techniques in a realistic manner. For comparison with the film example above, in the book of The Two Towers, Gandalf came not with Eomer's cavalry (who had joined King Theoden's forces earlier) but rather with a bunch of Huorns, against which the Orcs had no real defense. Also, Theoden did not wait for the enemy to enter his halls to use his cavalry, but made sorties several times through the battle, charging out and then retreating back to the Deep.
- And whereas in the film of The Return Of The King, the Rohirrim somehow easily routed the much bigger army of Orcs only to get completely thrashed by the enormous Mumakil (mounted elephants), in the book they spent most of the battle fighting other human cavalry and only took on the elephants when they had sufficient backup from Gondor.
The Belgariad and sequels/prequels, with emphasis on Algarian Light Cavalry and Mimbrate Arend Heavy Cavalry.
In Time Scout, like his Mongolian family, Skeeter can ride a horse in battle. One time, it was a trained warhorse.
Mounted combat is a staple of The Wheel of Time. Cavalry, both heavy and light, as well as mounted scouts are frequently important to various campaigns. For some nationalities, it's their hat.

Roleplaying Games

Generally not used in Dungeons and Dragons as mounts are usually significantly weaker than the characters, and can be killed, even accidentally, with Fireballs and other such attacks. However, the Mounted Combat chain of feats is very powerful, and paladins can summon a Cool Horse. (A druid or ranger's animal companion could be a horse, too, being more powerful than a regular horse, especially if ridden by a druid.)
- The drow use an interesting variant: instead of horses, they ride giant lizards.

Video Games

Age of Empires has cavalry used in various functions, often quite accurately pertaining to their function in real life. Light cavalry scout and chase down archers, knights are good against infantry and can also move fast to threaten archers, and are overall very powerful, expensive melee units, horse archers threaten slower-moving units, and there are a variety of special cavalry units unique to certain civilisations. All are vulnerable to spears.
Total War uses cavalry in different functions each game, as the setting and era changes each time and the games evolved themselves. A general rule of thumb from Shogun to Medieval II is that light cavalry flank and chase off archers, heavy cavalry see off lighter cavalry and can do the same roles better, with the exception of chasing archers, and horse archers stay away from foes and fire upon them out of range. Empire, of course, changes things again, being set in the age of gunpowder.
Fire Emblem has Cavaliers, Paladins, Great Knights, Nomads, Nomad Troopes, Rangers, Valkyries, and Mage Knights.
Mounted combat is an option in Koei's Dynasty Warriors and Samurai Warriors games. Some characters receive a great boost in fighting ability if they are mounted.
Mount & Blade is the single most realistic depiction of what actually fighting from horseback would be like in the video game industry, including horse archery and use of a lance in a battle.
Nethack allows you to ride pretty much any large animal you can tame. Unicorns, dragons, sky's the limit.