For someone new to the realm of boardgaming, let them try Carcassonne. This is a great introductory game for people who only associate board games with Monopoly, Risk, Clue, Scrabble etc etc.
Carcassonne is a tile-laying game where you lay down square-shaped tiles to build up Carcassonne and the area surrounding it. The tiles will allow you to build roads, castles and farmlands that help you score victory points.
The player with the most victory points at the end of the game wins. The game time is roughly 45 minutes and will likely reduce with more plays.
This is the base game, and expansions are available for those who want more variety.
This game is great value for money for the many hours of fun to be had by the whole family (and friends)! It is a great introduction to the world of Euro-style board games!!