Harmful Effects Defined
The term "Harmful Effects" is not actually defined by 5E, even though they use the term in several places. The closest we get to a definition is this:
Different attacks, damaging spells, and other harmful effects deal different types of damage.
so we go with the plain English definition. Harmful means:
causing or capable of causing harm
And Harm is defined as:
physical injury or mental damage;
Thus, we can conclude that "Harmful Effects" speaks specifically of things that can damage you. In short, by a strict usage of the English Language--that Shield Master feature applies against effects that...
- Only target you
- Require a Dex Save
- Deal Damage
This meshes with the Damage Types statement linked above, as it talks about Harmful Effects dealing types of damage.
I'm pulling all of these from Class Features, as they are the easiest to search
Feature works against
These class features meet all three criteria: They only target one person, require a Dex Save, and deal damage.
Storm Herald Barbarian's Storm Aura, Sea Option
When this effect is activated, you can choose one other creature you can see in your aura. The target must make a Dexterity saving throw. The target takes 1d6 lightning damage on a failed save, or half as much damage on a successful one.
Tempest Cleric's Wrath of the Storm
Also at 1st level, you can thunderously rebuke attackers. When a creature within 5 feet of you that you can see hits you with an attack, you can use your reaction to cause the creature to make a Dexterity saving throw. The creature takes 2d8 lightning or thunder damage (your choice) on a failed saving throw, and half as much damage on a successful one.
Arcane Archer's Seeking Arrow
[...]If the target is within the weapon’s range and there is a path large enough for the arrow to travel to the target, the target must make a Dexterity saving throw. Otherwise, the arrow disappears after traveling as far as it can. On a failed save, the target takes damage as if it were hit by the arrow, plus an extra 1d6 force damage, and you learn the target’s current location. On a successful save, the target takes half as much damage, and you don’t learn its location.
Monk, Way of Four elements: Water Whip
You can spend 2 ki points as an action to create a whip of water that shoves and pulls a creature to unbalance it. A creature that you can see that is within 30 feet of you must make a Dexterity saving throw. On a failed save, the creature takes 3d10 bludgeoning damage, plus an extra 1d10 bludgeoning damage for each additional ki point you spend[...]
Feature does not work against
In both of these examples, you are making a Dexterity Save to evade an effect that doesn't deal damage. Thus, the Shield Master feature does not aid you here.
Way of the Open Hand: Open Hand Technique
Whenever you hit a creature with one of the attacks granted by your Flurry of Blows
It must succeed on a Dexterity saving throw or be knocked prone.
Paladin Oath of the Ancients, Nature's Wrath
You can use your Channel Divinity to invoke primeval forces to ensnare a foe. As an action, you can cause spectral vines to spring up and reach for a creature within 10 feet of you that you can see. The creature must succeed on a Strength or Dexterity saving throw (its choice) or be restrained.