The only ways to disrupt someone's concentration are basically dealing damage or incapacitating/killing them. With the War Caster feat, dealing damage is unlikely to stop them, unless it's a STRONG hit.
I recently read that grappling someone incapacitates them, but without my book, it seems that grappling only stops them from moving. So are there any ways other than just dealing damage that cause concentration to end?
The rules explicitly point out that other situations may arise where a Concentration check needs to be made, based on the GM's assessment of a situation in the game.
In the description of Concentration (Basic Rules p. 79-80 ), the following comes after the three triggers for concentration to end: being incapacitated, damage and a failed Constitution save, or casting another spell which requires concentration.
The GM might also decide that certain environmental phenomena, such as a wave crashing over you while you’re on a storm‑tossed ship, require you to succeed on a DC 10 Constitution throw to maintain concentration on a spell.
These will be situational, and will follow the D&D 5e point of "rulings" where rules are not specific.
With that as a point of reference ...
a strong gust of wind knocking someone off their feet might trigger a DC 10 Constitution check if the GM deems it to be of sufficient impact on the concentrating creature.
Slipping and falling, depending upon the context, might do likewise. The GM may also raise or lower the DC depending upon the details of the situation or influence on the caster.
Spells
A few spells directly influence Concentration:
Sleet Storm (PHB, p. 276), influences Concentration, based on the spell save DC of the one casting Sleet Storm:
If a creature is concentrating in the spell’s area, the creature must make a successful Constitution saving throw a against your spell save DC or lose concentration.
Earthquake (PHB, p. 236) has an explicit influence on concentration if a failed save is made against that spell's DC.
The ground in the area becomes difficult terrain. Each creature on the ground that is concentrating must make a Constitution saving throw. On a failed save, the creature’s concentration is broken.
Storm of Vengeance(PHB, p. 279) has a similar effect but not with as explicit of a penalty:
Round 5–10. ... Each creature there takes 1d6 cold damage. Ranged weapon attacks in the area are impossible. The wind and rain count as a severe distraction for the purposes of maintaining concentration on spells.
That could be ruled as a disadvantage to the Concentration check the caster will make anyway, since the caster will be taking damage at this point in the spell. If the Warcaster feat gives Advantage to Concentration checks, this would neutralize that feature of the feat. (But it doesn't explicitly state that). Given that it is a high level spell (9th) I'd take that language in the spell description to favor a ruling of "Disadvantage" on the concentration check at that point in the spell's progression.
Note:(from PHB, p. 173 on Advantage & Disadvantage)
The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
The following Conditions (Basic Rules, Appendix A) create Incapacitation as a part of the Condition:
Stunned
Therefore, if the caster misses a save versus Petrification or Paralysis, or is subject to a sleep spell/sleep effect, whatever spell the caster is concentrating on ends.
As you noted in your question, the Grappled condition does not break concentration. But, if a character with the Grappler feat(PHB p. 167) and the Mage Slayer feat(PHB p. 168) grapples the caster in question, an interesting synergy arises:
The grappled spell caster has disadvantage on the concentration checks.
This leads to a higher likelihood of the concentration check being failed.
Convince the caster to end the spell. The fourth way that a caster ends concentration before a spell duration expires is to choose to stop concentrating. A Suggestion or Charm spell, or an effect similar to those spells, could induce a caster to stop concentrating in a spell.
Out of combat, something like a bribe or a persuasion attempt, or an intimidation attempt, could do similarly. This again is a situation-dependent interaction.
Note that being grappled does not break concentration. Also, polymorphing or taking beast shape does not break it.
As a PC trying to break the concentration of a foe, your best bet is damage. Either do a lot of it in one go (causing a difficult save) or do it in a lot of attacks (causing lots of saves, hoping one of them will fail). A good spell for this is magic missile, where every missile causes a concentration check.
Alternatively, incapacitate them with spells like sleep.
The caster can decide to willingly end concentration at any time (on anyone's turn, if in combat).
So another option for the PC trying to break the foes' concentration is to coerce, trick or bribe the foe to do it willingly.
Also note that "ending concentration" and "having concentration broken" are two different things. For example the spell conjure elemental, having concentration broken means the elemental goes rogue but ending concentration simply unsummons the elemental. (Hat-tip V2Blast.)
There are three methods mentioned in the rules to interrupt a spell with a duration of concentration:
Outside of these three methods, there are no ways to interrupt concentration.
