OK, just sayin', this is a good question.
Starting things off, Adamant and Modest are good on sweepers that aren't meant to be fast or that boost their Speed/use priority. For example, Azumarill runs HP, Attack, and Adamant with its Belly Drum + Sitrus Berry + Aqua Jet set, since it doesn't need Jolly and Aqua Jet usually.
Another example is a fast Swift Swim/Sand Rush/Slush Rush/Chlorophyll user. Barraskewda doesn't run Jolly on rain teams because of its insane Speed with 252 EVs and Swift Swim, it basically always runs Adamant. Kingdra also runs Modest over Timid.
Another obvious example would be TR teams, though you would prefer Brave/Quiet over Modest or Adamant (Modest is still a good option on TR teams though, since as a Special Attacker you usually want to take minimal damage from Confusion and Foul Play).
Some Choice Scarf Pokemon will also run Modest or Adamant, especially if they are naturally fast and just use a Choice Scarf for outspeeding a few threats.
Oh, to elaborate on Pokemon who boost their Speed, some Scolipede's, Blaziken's, or Sharpedo's may run Adamant, though it's not quite that common.
Also Pokemon who just have terrible Speed and there's no point in boosting it (Galarian Slowbro is a good example).
Hope this helps! :)