Some spells can push the target X feet away (like thunderwave, which pushes 10 feet away on a failed save). I was wondering what happens if the target, while being pushed, encounters a wall or other rigid object. Does it take (bludgeoning) damage? To me it seems logical that it would: it is like falling, sudden force applied to a creature due to encountering resistance from an object.
I couldn't find any rules about this in the Player's Handbook nor online.
Spells do what they say. The spell doesn't say they take damage if they cannot move 10 feet so they don't.
This is in line with falling damage as no damage is taken for falls less than 10 feet. Now, if you use such a spell to push them off a cliff ...
This is one of those cases where a couple of D&D rules analysis clichés apply, though they still deserve explication: spells do what they say they do, and D&D is not a physics simulator. These are important because they offer the most direct way to consider such an effect from such a spell. In the absence of a specific rule stating that this is or is not possible we have to look at rules that do exist for guidance, at least as a first-order investigation. Let's take those in turn:
Spells do what they say they do
This one is pretty straightforward. Spells that contain text about forced movement, like Thunderwave, don't say anything about situational or environmental damage. There aren't many that I can think of offhand (Thunderwave, Eldritch Blast with the Repelling Blast invocation, and Telekinesis all push or can push, and Thorn Whip and Eldritch Blast with the Grasp of Hadar invocation can pull), and none of them contain such text.
We can also look at the rules' description of how damage from spells is defined:
A spell tells you which dice to roll for damage and whether to add any modifiers. (PHB, Chapter 9: Combat, Damage and Healing, Damage Rolls)
If a spell doesn't tell you to to roll a damage die, you don't roll it. If the spell's effects trigger some other defined mechanic (like being moved off of a cliff, after which the moved creature or object falls ten or more feet), then you would adjudicate that other mechanic as the rules define it. Both of those are absent in the case of being moved into a wall.
This isn't great evidence that a secondary effect, like impact against a surface, cannot occur. But the key point to draw here is that we have no resources (from the spell descriptions themselves) to guide our thinking on how to implement those effects in a generic sense. What damage die would be the right one to pick? Does the material the wall is made of make a difference? What about the size of the creature? The spells don't touch these details at all, and parsimony suggests that reading such effects into the spells is not the right approach.
D&D is not a physics simulator
This item completely addresses the sole argument presented in the question that collision damage should exist:
To me it seems logical that it would: it is like falling, sudden force applied to a creature due to encountering resistance from an object.
In the real world, this is 100% correct. But the real world doesn't contain Eldritch Blasts or Thunderwaves, so real-world considerations may not be the best way to understand in-game circumstances.
Even if you don't like that approach, the game rules do not deal with most of the relevant details either:
Whether or not you want to model these kinds of interactions in the game, the official rules do not provide enough detail to apply them. The game is instead a set of simplified mechanics which simulate some specific things and not others, while also simulating some decidedly unreal things.
As pointed out in the question, forced movement from one of these spells seems similar to mechanics for falling. That's as close as we can get because there are no published rules for being bashed against a solid surface. The PHB describes damage from falling as
At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall. (PHB, Chapter 8: Adventuring, The Environment, Falling)
The damage doesn't occur because it's realistic-- it occurs because the rules state it. It is pretty clear that falls of less than 10 feet do no damage (which is itself not realistic; I've sprained my ankle from falling way less than that!). Falling from 15 feet is exactly as dangerous as falling from 10 feet, or 19 feet, or 11 feet. Realism is not a factor.
In that light, the lack of a rule describing being slammed into walls by forced movement is conclusive. There is no rule, so there is no damage.
We have a few other indications in the rules of hitting walls (or sort-of-walls hitting you) not having the most realistic effects:
The Rolling Sphere trap description in the DMG states
Activation of the sphere [a 10-foot-diameter rolling sphere of solid stone] requires all creatures present to roll initiative. The sphere rolls initiative with a +8 bonus. On its turn, it moves 60 feet in a straight line. The sphere can move through creatures’ spaces, and creatures can move through its space, treating it as difficult terrain. Whenever the sphere enters a creature’s space or a creature enters its space while it’s rolling, that creature must succeed on a DC 15 Dexterity saving throw or take 55 (10d10) bludgeoning damage and be knocked prone.
The sphere stops when it hits a wall or similar barrier. It can’t go around corners, but smart dungeon builders incorporate gentle, curving turns into nearby passages that allow the sphere to keep moving. (DMG, Chapter 5: Adventure Environments, Traps, Rolling Sphere)
It doesn't matter what the wall or barrier is made of, nor what the sphere is made of, nor that the sphere is moving at ten feet per second. The sphere stops completely on contact with the wall or barrier.
There is an interesting, similar case in the Sphere of Crushing Doom:
The trap’s active element is a sphere of steel that almost fills the 10-foot width of the hallway and rolls to the bottom of the slope on its turn. Each creature in the sphere’s path must make a DC 20 Strength saving throw. On a failed save, a creature takes 22 (4d10) bludgeoning damage and is knocked prone. On a successful save, a creature takes half as much damage and isn’t knocked prone. Objects that block the sphere, such as a conjured wall, take maximum damage from the impact. (Xanathar's Guide to Everything, Chapter 2: Traps Revisited, Example Complex Traps, Sphere of Crushing Doom)
When the sphere is made of solid steel, as opposed to solid stone, a wall that it hits takes damage but the sphere does not. This is at least an example of a lateral impact with a wall causing bludgeoning damage, and is the closest support for collision damage I can find. Whether or not a given creature is more durable than a giant, solid ball of steel is another question (and one which is probably not too solidly answered by the rules as written).
1d6 damage isn't so much that it risks breaking the game, and isn't wildly out of line with damage that attack cantrips deal (especially when characters reach a high enough level to get extra damage dice), and is pretty conditional in when it can be applied. It also never gets better, as the maximum forced movement from these spells is ten feet. There may be unintended consequences of a ruling in this direction with other game mechanics, but that's out of scope here.
Importantly, it isn't so good that players will be driven to force enemies to within ten feet of walls to set this collision up or use a spell slot on Thunderwave rather than something else that might be situationally valuable. But it is cool and dramatic enough that players might be excited to get the extra damage when the opportunity arises organically.
