Over the years, my favorite games have been multi-player “party” games with creative/expressive mechanics: Charades, Pictionary, Scattergories, Scrabble, … (not necessarily in that order). From the point of view of mechanics, they have some key features in common:

• The core mechanic is simple and familiar: gesturing in Charades; sketching in Pictionary; thinking of and writing words in Scattergories; forming words from a set of letters in Scrabble.
• They are turn-based, usually with a time limit (though not always).
• There are many “right” ways to successfully accomplish the core mechanic: e.g. different gestures or drawings to convey a term in Charades and Pictionary; different words that can match the given category in Scattergories; etc.
• There is an element of luck (being assigned an easier/harder term, category, or set of letters …), but success primarily depends on the player’s skill, which can be improved with practice.
• The player’s attempted solution on each turn must be validated/arbitrated by other players: teammates have to guess the correct term in Charades and Pictionary; other players must agree to the validity of words produced in Scattergories & Scrabble; etc. This leads to a lot of interesting (and fun to resolve!) disputes, which require frequent reexamination of the formal constraints.