This answer only lists the otherwise unlisted effects of each condition that could apply to practically any character (that I could find, of course).
It does not include class-specific examples, race-specific examples, feat-specific examples or other such things. Similarly it does not include monster-specific examples. An example of something not included here is that a Barbarian cannot benefit from Danger Sense while Incapacitated.
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 for inclusion.
Grappled
- Technically, being grappled also affects the grappler since their speed might be halved (depending on creature sizes) (PHB, p. 195, "Grappling–Moving a Grappled Creature").
Incapacitated
An incapacitated creature does not count towards flanking (an optional rule from page 251 of the Dungeon Master's Guide).
An incapacitated creature does not cause disadvantage on ranged attacks in close combat (PHB, p. 195, "Ranged Attacks In Close Combat").
An incapacitated creature can automatically be grappled (PHB, p. 195, "Grappling") and automatically be shoved.
An incapacitated creature loses concentration on spells (PHB, p. 203, "Concentration–Being incapacitated or killed").
An incapacitated creature cannot take actions, which also prevents them from taking bonus actions (PHB, p. 189, "Bonus Actions").
Invisible
- An invisible creature can always try to hide (PHB, p. 177, "Hiding").
Prone
The prone condition does not describe what crawling actually means; instead, crawling is described under "Special Types of Movement" (PHB, p. 182, "Climbing, Swimming, and Crawling") and "Being Prone" (PHB, p. 190) under "Movement and Position" in the combat rules.
A flying creature that is knocked prone falls unless it can hover or is flying by magic (PHB, p. 191, "Flying Movement").
A mounted creature that is knocked prone, must make a saving throw (PHB, p. 198, "Mounting and Dismounting").
If your mount is knocked prone, you can use your reaction to land on your feet (PHB, p. 198, "Mounting and Dismounting").
Unconscious
- An unconscious creature can be stabilized (PHB, p. 197, "Stabilizing a Creature").
