When you are attacking an object or vehicle
Many hard objects (DMG 247) and large vehicles (DMG 119) have damage thresholds, and don't take any damage from attacks that do less than this amount.
When the damage type or damage source matters
This isn't a function of the amount of damage per se, so not really a direct answer to the question, but there will often be a tradeoff, especially for casters, between spells that do a single amount of damage and spells that do smaller amounts of damage with multiple hits that total more. In general the total damage is the better option, until one considers the damage type or damage source.
For example, for a first level slot one could cast three magic missiles for a total average damage of 10.5, or one chromatic orb with an average damage of 9 (12.5 with a 75% chance to hit), but you have a choice of one of six damage types, to which the target might be vulnerable. For a second level slot, you could shoot three scorching rays with a total average damage of 14 - but if the target is immune to fire, a single acid arrow for less damage on average would be better.
When the rounding loss from damage resistance approaches the amount of damage that can be done
Suppose you are attacking a barbarian and have the choice of a single weapon that does 1d6 or two weapons that, dual-wielded, both do 1d3. Clearly 2d3 (individual average damage 2, total average damage 4) is more than 1d6 (average damage 3.5).
However, suppose the barbarian then enrages, such that all three weapons will be subject to their damage resistance. If the damage was just halved, the two attacks would still be better, but in 5e we always round down to integers unless otherwise directed, so a rolled 1 for damage will be treated as no damage after rounding down. In this case the average damage of the d6 becomes (0,1,1,2,2,3) = 1.5 while the average damage of 1d3 is (0,1,1) = 2/3. In this case the average damage of the 2d3 subjected to resistance is now less than that of the d6, and you would be better off using the single weapon for a single, large hit rather than the two weapons for two, smaller hits since they no longer total more.
This effect goes away for 'larger' dice since the chance of a rolled one becoming zero is less. Given the choice between a two-handed spear (1d8) and two daggers (2d4), the daggers are better before resistance but both options are equal after resistance (average damage 2). For larger weapons the two attacks would remain better even after resistance.