fully cooperative: Hanabi, The Crew, The Captain Is Dead, Pandemic
partially cooperative: Red November, Betrayal at House on the Hill (original and Legacy), Dead of Winter, Gloomhaven
competitive [...] strongly mutually beneficial deals: Catan, Diplomacy, 18XX (and almost any other game where players own stock in each other’s positions)
competitive [...] placement in each round matters: Power Grid, 18XX,
competitive [...] not usually permanent alliances are critical to victory: Diplomacy, Twilight Imperium (all of them), Cosmic Encounter
These are just the ones I’ve played in recent memory. I’d wager I can name 20 games in each category, with some overlap like above, with more time to think and research.
When characters pick up gold and items, they can’t be shared, so there’s sometimes a race to get them, and players might not work for the benefit of the whole party at that point.
Every session/scenario/map, each character gets a secret goal with a small character progression bonus for achieving it, and pursuing those often requires making one to a few selfish choices.
Also for the lifetime of a character there’s one secret goal, which again inspires some selfish choices on a longer timeline.