Oh! I just recalled that we also have FATEs and just plain overwolrd enemies dedicacted to that matter!
Right now mainly the poachers and the related questline in the South Shroud are coming to mind aswell as the shady characters in Southern Thanlan, just outside of the Amalj'aa area (and their respective FATE... that was included in one of the relic books... with an aweful long spawntimer... the real crime here!)

If you take a look at Sastasha, you'll also find kidnapped women around there - and Tam Tara is obviously home to a Dalamud cult.