Mounted Missile Combat

[ZorroGames]

Weapons useful for mounted missile combat?

Yes:

Javelin?
Spear?
Crossbow, Light?
Dart?
Shortbow?
Hand Crossbow?
Heavy Crossbow?

No:

Sling?
Blowgun?
Longbow?
Trident?

Maybe:

Dagger?
Handaxe?
Light Hammer?
Net?

[Sir cryosin]

Weapons useful for mounted missile combat?

Yes:

Javelin?
Spear?
Crossbow, Light?
Dart?
Shortbow?
Hand Crossbow?
Heavy Crossbow?

No:

Sling?
Blowgun?
Longbow?
Trident?

Maybe:

Dagger?
Handaxe?
Light Hammer?
Net?

Ok so samurai's are horse back longbow man. Slings are pretty easy to use on horse back as well. Javelins have been used on horseback so has shortbows and Spears. Crossbows maybe but it would be difficult to reload and take longer if are on horseback. Nets light hammers are useable as well. Darts are useable but are a really neish weapon. Hand axes sure but there are better things. Blowguns are pretty long for the most part but they come in smaller sizes but still the same as darts. Dagger is a no go to short. Trident would be used as a spear but falls under the dart and blow gun

[Lalliman]

In what context are you asking? Game mechanics? Pretty sure they all work. There's nothing that says they don't.

Realistically?

All bows and crossbows are feasible, though it takes special training. Longbows seem awkward as hell to use mounted, but I believe the Japanese did it, though with a modified longbow design.

Dart, dagger, handaxe and light hammer, I don't see why not.

Javelin, spear and trident seem awkward. You generally use a lot more than just your arm to throw those effectively. I don't feel like you could get a lot of distance with your range of movement limited by being on a horse.

Slings should work. In real life you have long and short variants, for long and short range, though this isn't represented in D&D. The short variant should work just fine. Long variant, you'd have to be careful not to entangle your horse's legs, but it's probably doable for a trained user.

Blowgun... I'd be afraid of inhaling the dart due to the turbulence of riding a horse.

Do I even need to address the net? Would be a great way to entangle your own horse.

[Lombra]

In-game: longbow (or hand crossbow with some fancy feats)
IRL: either a crossbow or a shortbow.

[JackPhoenix]

RAW, any weapon works.

In my game, I give Heavy weapons disadvantage to attack when mounted, melee and ranged.

[Vaz]

Eldritch Blast? /thread?

[Corran]

If you are doing it any other way than a shortbow/longbow, then you are doing it WRONG!
ps: Javelins allowed too, I guess....

[Slipperychicken]

"Realistically", mounted javelin-throwers were absolutely a thing in real life, and saw use in war, particularly among skirmishers.

Lassos and nets have likewise been used from horseback against both humans and other animals.

[CaptainSarathai]

Everyone talking about Samurai and mounted longbows: you need to understand something.

The English Longbow was enormous, 6' from tip to tip, and it had a draw weight of at least 100lbs. No other culture on in the world, except arguably India, used bows this large and this powerful. Partially because they simply didn't have the right quality of wood for it.
Moreover, when you fire a longbow, you don't hold the bow and pull the string. You hold the string and push the bow. This technique has been passed down and was recorded fr the time of Henry VII. You can't do that from horseback.
The Samurai use an asymmetrical bow, the daikyu and hankyu (long and short, respectively). They are recurve, wood-and-bamboo laminate bows, and they usually draw at around 70lbs for a war-bow. Contrary to popular belief, the interesting off-center grip predates the use of the bow from horseback, and is actually done to help with the strength of the bow, as the strength and flexibility of wood differs as you go up the tree - offsetting the grip balanced this out.
Yumi style bows were powerful for being a wooden bow, and for use from horseback. Not as powerful as an English longbow, or the bone laminated bows of the Asian steppe, but still quite respectable. In terms of range and impact though, they are absolutely not longbows, and are more comparable to the smaller bows used by other nations.
(Note: the Japanese are an insular country. They were not part of the global arms race to take up new traditions and weaponry. If a bow was legendary in Japan, it's because it was able to penetrate Japanese armor, which only had to defend against Japanese weapons and style of attacks. It made them very slow to adapt, and their weapons and equipment are generally not as "amazing" as we like to think)
--
To answer OPs question
I would say that your typical ranged weapons from horseback would be:

Definite:
Short Bow
Javelin/Spear/trident

Maybe:
Hand crossbow
Light crossbow
Throwing axe

The issue you face with crossbows is the same issue that the French discovered when using them is sieges: there's nothing holding the bolt in place. If you point a crossbow downward, the bolt will slide out. Unlike a bow, when you load a crossbow, you bring the string back to full draw and then slot the bolt into it.
Hand crossbows and some light crossbows had a lever which would catch and draw the string. Heavy crossbows (such as those used by the French) needed to be braced against the foot, have a winch attached, and wind the string back. This would be nearly impossible from horseback.

An interesting note is that no thrown weapon is as powerful from horseback as it is on foot. The thrower just can't get enough body behind. Missile weapons designed to use from horseback were also usually made less powerful, to make it easier to draw and aim while also riding.
This was offset by the fact that cavalry can get into closer range than infantry, with less personal risk. Imagine Napoleon's lancers during the revolution; they often carried pistols with them, rather than rifles. Rifles were powerful, and that added power gave them a longer range and greater accuracy. Infantry could fire their rifle far enough away that they'd have time to reload and shoot again before enemy infantry could bring them to melee. An infantryman firing at pistol range is going to find himself in danger of being clubbed to death moments later. But a cavalryman... he can ride up to your lines, blast you right in the face with that pistol, and then happily gallop away to reload, and you can't catch him. This kind of rotating hit-and-run attack is what made cavalry so powerful on the battlefield. The idea of "impact cavalry" (armored knights going knee-to-knee and charging with lances) was unique almost exclusively to Europe, and was only a viable tactic for a comparatively "[I]blink and you've missed it" portion of cavalry history.

[Floopay]

Weapons useful for mounted missile combat?

Yes:

Javelin?
Spear?
Crossbow, Light?
Dart?
Shortbow?
Hand Crossbow?
Heavy Crossbow?

No:

Sling?
Blowgun?
Longbow?
Trident?

Maybe:

Dagger?
Handaxe?
Light Hammer?
Net?

I had a character who chained harpoons to his celestial mount's saddle, and would spear enemies and drag them to death.

A net could be used in a similar fashion. Catch an enemy, and then drag them to death.

Tridents are typically used in the other direction. Designed to essentially take someone off a mount, and they might do just that to the wiedler if they hit someone hard enough while charging on your mount.

Longbow would be okay if they kept a slow pace and distance. Essentially using the horse more to keep distance than anything else; but I would definitely say the handaxe and dagger are out. Light hammer seems like a mace, where the user is just using the weight of it and the momentum of the horse to do damage.

Thanks for reading,
Floopay

[Vaz]

An interesting note is that no thrown weapon is as powerful from horseback as it is on foot. The thrower just can't get enough body behind. Missile weapons designed to use from horseback were also usually made less powerful, to make it easier to draw and aim while also riding.
This was offset by the fact that cavalry can get into closer range than infantry, with less personal risk. Imagine Napoleon's lancers during the revolution; they often carried pistols with them, rather than rifles. Rifles were powerful, and that added power gave them a longer range and greater accuracy. Infantry could fire their rifle far enough away that they'd have time to reload and shoot again before enemy infantry could bring them to melee. An infantryman firing at pistol range is going to find himself in danger of being clubbed to death moments later. But a cavalryman... he can ride up to your lines, blast you right in the face with that pistol, and then happily gallop away to reload, and you can't catch him. This kind of rotating hit-and-run attack is what made cavalry so powerful on the battlefield. The idea of "impact cavalry" (armored knights going knee-to-knee and charging with lances) was unique almost exclusively to Europe, and was only a viable tactic for a comparatively "[I]blink and you've missed it" portion of cavalry history.

If by "unique almost exclusively", you mean not at all unique, sure. The Klibanophoroi and earlier Cataphractii are found as far east as India. And if you mean by "blink and you've missed it", from at least Philip II of Macedon to the Napoleonic War, sure.