To be fair I wrote the answer, then figured “surely somebody else must’ve written an answer by now”, refreshed, saw two other answers (one 12 seconds old), thought “fuck it” and posted anyway. They’re all written a bit differently so maybe some are easier to understand than others.
In my experience the most popular and fun “party games” are boardgames such as Top Ten, Time’s Up, Hot & Cold or Codenames (more or less in that order). They work best for 6 to 10 players. Though I don’t think they shine in a highly competitive tournament setting.
Randomness exists in all of these games but I consider it very balanced/smoothed out so it shouldn’t really affect the outcome. Not all of the games I mentioned have permanent teams, but that can easily be changed with house rules.