Is there any rule that says you must use cantrips at the full force your level allows?  If my 5th level sorc only wants to throw a 1d10 Firebolt, or a Warlock only wants to throw a single Eldritch Blast, is this an option by RAW?

Could I theoretically throw only, like, two or four dice of a Fireball or similar spell?

I can't imagine a DM telling me I can't choose to self-nerf, but I'm wondering if it's officially legal.

As you likely expect, RaW doesn't allow for it, so it would be DM ruling.  I, as a DM would need a strong and viable explanation of why and how you would intend to do this.  Initially I would rule that no, you can not "downcast" a spell below it's level as listed.  That's because the magic that is created is based on (magical rule-y garble) and manifests in at LEAST this fashion.  Cantrips and their scaling, turn into a weird one, with EB being an exception.  You can fire all the bolts at different targets, so if you wanted to hit the foe with one, you could shoot a rock with the rest.  Fireball, however, is written to deliver a blast doing X damage, and scaling UP from there.  This indicates a base the spell effect can occur at.

It's significantly different in application and theory, from melee attacks, where it is quite easy to pull a punch.  Spells and magic tend more toward, maybe gunpowder.  It goes off and causes X amount of damage/noise and so forth.  It can't cause less, because that is where it starts.  A punch can technically start with a gentle touch to the chin, then slowly escalate to a blow that would break the jaw.

IMHO, you're here asking this question precisely because you imagined a DM telling you that you can't choose to self-nerf. And no, RAW doesn't support what you're asking to do. 

On the current battlefield, there are technologies and delivery methods that limit the risk to human life, at least from the user's standpoint. By removing the risk to human life some might point out that these methods will be used more and lend themselves to more physical conflict instead of diplomatic recourse. This is in the same vein. Very careful consideration should be had before unleashing the primal powers of the universe, for we are but human and prone to oversight and negligence.

Magic is supposed to be a powerful and dangerous tool to wield. Much like the gunpowder analogy, once the weapon is fired, anything in the path of the projectile is a target. Even the unintended backstop. That said, I would agree that pulling punches magically or with ranged weapons isn't allowed RAW, but if your DM wanted to allow it with a Hard or Very Hard Arcana check or maybe disadvantage for ranged weapons, that might be feasible.  

Quote from FoxfireInferno9 >>

Is there any rule that says you must use cantrips at the full force your level allows?  If my 5th level sorc only wants to throw a 1d10 Firebolt, or a Warlock only wants to throw a single Eldritch Blast, is this an option by RAW?

Could I theoretically throw only, like, two or four dice of a Fireball or similar spell?

I can't imagine a DM telling me I can't choose to self-nerf, but I'm wondering if it's officially legal.

It would depend entirely on the spell in question - there's no generic rule in the game letting you simulate being at a lower level (for cantrips) or cast at a lower spell level (for leveled spells).  None of the specific spells you listed have it, but theoretically, any spell could be written to have it.

I'll use Fire Bolt as my example:

• Current text (where the increased damage is mandatory):  This spell's damage increases by 1d10 when you reach 5th level (2d10), 11th level (3d10), and 17th level (4d10).
• Replacement text that would make it an optional effect:  You can increase this spell's damage by 1d10 when you reach 5th level (2d10), 11th level (3d10), and 17th level (4d10).

For melee attacks you can declare you're delivering non-lethal damage by trying to knock someone out, but I don't think it applies to spells. I can't think of any other scenario in which you'd want to do this.

I guess the RP behind it would be "I don't want to put my full magical energy into it, can I throw it at reduced force?"

As a DM I'd allow it.

 One obvious reason to desire to reduce the amount of damage a spell does is when you ar ecasting it on an ally to attempt to get out out of a spell.
Say a party member has had Dominate person cast on them. They get to reroll the save whenever they take damage so you want them to take damage but take as little as possibe.

Some spells are melee spell attacks. RAW you can't reduce the amount of damage you do with them, but you can decide to use them to knock someone out instead of doing lethal damage if you want.

Knocking a Creature Out

Sometimes an attacker wants to incapacitate a foe, rather than deal a killing blow. When an attacker reduces a creature to 0 hit points with a melee attack, the attacker can knock the creature out. The attacker can make this choice the instant the damage is dealt. The creature falls unconscious and is stable.

Imagine using Blade of Disaster to just knock people out.

I think the best way of incapacitating a creature without killing it, particularly for a story purpose in your game, is to tell the DM what you are trying to do and see if they choose to give the creature death saving throws when it reaches 0 hit points. Then you can stabilize the creature just as you would with a player. This is discussed in the rules, but most of the time DMs simply keep the game moving by skipping death saves for NPCs unless there is a reason to have them.

Quote from Kaavel >>

Magic is supposed to be a powerful and dangerous tool to wield.  

 This is my take. Being able to "downcast" fireball significantly changes the feel/lore of the spell IMO. This kind of thing has a very profound effect on the relationship between people & magic in your campaign. In some games it might be appropriate, in some it might not.

My DM allows it for cantrips. Like the magic version of choosing ribbon-lethal damage with a hit, but instead of “non lethal,” just less. But only on cantrips though.