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The Create Bonfire cantrip creates a bonfire which "fills a 5 foot cube". It deals comparable damage to other cantrips, making one assume it's meant to only deal it (reliably) to a single target. But, if playing on a grid, is there something actually preventing a character from making the 5 foot cube be placed at an intersection, possibly damaging four creatures?

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Technically, there's nothing preventing it

DMG, Areas of Effect on Grids (p.251)

Choose an intersection of squares or hexes as the point of origin of an area of effect, then follow its rules as normal. If an area of effect is circular and covers at least half a square, it affects that square.

There's a few interesting points here- namely, that the point of origin specifically targets the intersection between squares. Since there are no exceptions made for a cube-based AoE, by RAW it would seem that you could place the origin of the cube face at a corner and angle it diagonally, resulting in 5 squares containing fire.

Also note that there is no rule that requires "half the square to be covered" by the effect- that clause only applies to circular area of effects. (As @RevenantBacon points out, this may also be interpreted to say that for non-circular spells, the entire square must be covered to have an effect- in which case this gambit would be entirely ineffective.)

I don't see anything in the rules that directly prevents this from working- though note there is also no rule that says "if any part of a square is covered by a non-circular effect, then the entire square is affected.".

But

As the question recognizes, this is clearly not the intent of the spell. The grid is only an approximation, and the angle at which you cast a spell should not result in a drastic increase in the number of squares effected. Additionally, ruling that it works this way requires that all non-circular AoE effects can affect tiles they only barely clip through, which increases the area for many, many spells.

Also, any player who suggests this during play is likely going to get several skeptical glances and then promptly shot down, at best.

A reasonable ruling would be to use the rule on circular areas as guidance, and rule that if an area does not cover at least half of a square, it has no effect.

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    \$\begingroup\$ For the record, DM allowed it, which hey, I've no problem with. It's our warlock's signature spell, so why not. \$\endgroup\$ – vonBoomslang Apr 10 at 20:59
  • \$\begingroup\$ I believe the "circular spells that cover at least half the square" is phrased in such a way that t is an exception to the general rule that a spell otherwise would not affect that square. \$\endgroup\$ – RevenantBacon Apr 10 at 21:02
  • \$\begingroup\$ @Rev That's a reasonable reading; in fact, I think I prefer it to the alternative. I'll edit that in as a note in my answer. However, since there's no general rule for this to override, I don't think it's unambiguous. \$\endgroup\$ – Carcosa Apr 10 at 21:07
  • \$\begingroup\$ " it would seem that you could place the origin of the cube face at a corner and angle it diagonally, resulting in 5 squares containing fire." How does that work? \$\endgroup\$ – Mark Wells Apr 10 at 21:12
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    \$\begingroup\$ @Mark Here is a very quick drawing of the targeting required. Note that two of the squares contain almost no fire. \$\endgroup\$ – Carcosa Apr 10 at 21:29
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No.

The first thing you need to remember is that while a medium (or small) creature uses a 5-foot square in combat, it does not actually fill that full 5-foot volume (unless it's, say, a medium Gelatinous Cube that exactly fills a 5'x5'x5' area).

If you were to have Bonfire cast on an intersection so that it partially filled 4 different squares, you'd only be filling 1/4 of any given creatures square. You'd be unlikely to affect any of the 4 creatures occupying those squares, as they would have plenty of room to stand/maneuver in the remaining 3/4 of their square without having to worry in the slightest about the fire.

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    \$\begingroup\$ -1 As mentioned below by RAW "Choose an intersection of squares or hexes as the point of origin of an area of effect". If the spell effect covers part of the square, any creature in that square becomes a target of that spell. There is no mechanic in RAW that says you can prevent a spell-effect from affecting you because you are tipee-toeing on the edge of a 5' square to avoid an effect. \$\endgroup\$ – Senmurv Apr 10 at 22:51
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    \$\begingroup\$ @Senmurv "If an area of effect is circular and covers at least half a square, it affects that square." That at least strongly implies that if a square effect covers only a quarter of the square, it should not necessarily target creatures in that square. \$\endgroup\$ – Ben Barden Apr 10 at 22:55
  • \$\begingroup\$ @Senmurv Except they don't need to "tipee-toeing on the edge of a 5' square" (as you so sarcastically put it) to avoid the effect. They have plenty of space in the rest of the square. There simply isn't enough of the effect present in the square to provide a significant effect. \$\endgroup\$ – RevenantBacon Apr 11 at 4:25

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