Let's analyze each group to determine the odd word out:
1. dull - tiring - awful - fun: The odd word is "fun" because the other three words (dull, tiring, awful) have negative connotations, while "fun" has a positive one.
2. dominoes - painting - backgammon - billiards: The odd word is "painting" because the other three words (dominoes, backgammon, billiards) are games.
3. good - fond - keen - bad: The odd word is "bad" because the other three words (good, fond, keen) have positive connotations, while "bad" has a negative one.
4. rarely - quick - never - always: The odd word is "quick" because the other three words (rarely, never, always) are adverbs of frequency, while "quick" is an adjective related to speed.