The Skaven have a habit of repeating some words (yes-yes! run-run!) and call other races as (name)-things, like "Man-things"
As shown in the novel Grey Seer, they also often put words together when speaking in Queekish (kill-slay, traitor-meat, see-smell etc.). Jeremias Scrivener speaks the same way when challenging Thanquol in Queekish, so this seems to be a trait of the language.
In Legend of the Five Rings, a race of rat-people known as Ratkin tend to repeat random words when speaking Rokugani. Towards the end of their regular appearances in the story, this was scaled back as the players were getting sick of it (although some of their later appearances retain the quirk).
In Dungeons & Dragons, some players (and DMs) who roleplay kobolds tend to have them saying "meep!" with almost every line, often with a fair amount of Hulk Speak for good measure.