This answer only lists unlisted effects of conditions that could apply to practically any character and does not include class-specific examples, race-specific examples, or other similar things. The fact that a Barbarian cannot benefit from Danger Sense while Incapacitated is an example of something that is not included here.

Some of the things below are also *extreme* technicalities; I opted to include everything I found instead of trying to make some sort of cutoff.

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* Grappled

1. Technically, being grappled also affects the *grappler* since [their speed might be halved][2] (depending on creature sizes).

* Incapacitated

1. An incapacitated creatures does not count towards flanking.

1. An incapacitated creature [does not cause disadvantage on ranged attacks in close combat][1].

1. An incapacitated creature can [automatically be grappled][2] and [automatically be shoved][3]

1. An incapacitated creature [loses concentration on spells][4].

* Invisible

1. An invisible creature [can always try to hide][5]

* Prone

1. The prone condition does not describe what [crawling][6] actually means.

1. A flying creature that is knocked prone [falls unless it can hover or is flying by magic][7]

1. A mounted creature that is knocked prone, [must make a saving throw][8].

1. If your mount is [knocked prone, you can use your reaction to land on your feet][8].

* Unconscious

1. An unconscious creature [can be stabilized][9]

[1]: https://www.dndbeyond.com/sources/basic-rules/combat#RangedAttacksinCloseCombat
[2]: https://www.dndbeyond.com/sources/basic-rules/combat#Grappling
[3]: https://www.dndbeyond.com/sources/basic-rules/combat#ShovingaCreature
[4]: https://www.dndbeyond.com/sources/basic-rules/spellcasting#Concentration
[5]: https://www.dndbeyond.com/sources/basic-rules/using-ability-scores#Initiative
[6]: https://www.dndbeyond.com/sources/basic-rules/adventuring#ClimbingSwimmingandCrawling
[7]: https://www.dndbeyond.com/sources/basic-rules/combat#FlyingMovement
[8]: https://www.dndbeyond.com/sources/basic-rules/combat#MountingandDismounting
[9]: https://www.dndbeyond.com/sources/basic-rules/combat#StabilizingaCreature