You've played Monopoly, Cluedo and Risk. You may have played Ticket to Ride, Settlers of Catan and Carcassonne. Each of these games are great in their own way and are great for families to play. The latter three games are the least divisive and have many different strategies available to win which make them games you want to play again and again.
Dixit is a game unlike any of these games. In fact it is unlike any other game I have ever played before or since. Each time you play the game it becomes both easier and more difficult. It's a very subtle game that pulls on your creative thinking. Trying to work out what phrase (or mime etc.) for a particular picture will spark an equal response from some of your fellow players, but crucially not all, is what makes this game challenging. Too subtle and your friends miss the connection. Too obvious and you are penalised. Please do not to let this put you off. Dixit is a game that has intrigue in every round. Trying to guess the Storyteller's card is not straight forward. Each other player gives in a card that they think best represents the given phrase and they are shuffled before being revealed. With one card per player it can be difficult to distinguish the Storyteller's cards from the charlatans.
The most recent time I played there were eight of us, aged between 28 and 60. There were only five takers for the game; the remaining three were seemingly more interested with their mobile phone or tablet devices and let the rest of us play. As soon as the cards were revealed in the first round they downed their electronics and were enthralled by the game. Each of them tried to guess at the Storyteller's card and even helped their partner during the game. Much like other reviewers have said, the scoring is not the most important aspect of this game. I have never once seen an argument playing this game, and I do not expect I will. I have even played with my family who cannot get through a game of Monopoly without at least two people storming off or the board being launched at the nearest wall.
Should you buy this game? If you want a game that is relaxing yet though provoking, creative while lacking a need for strategic thought and a game without conflict then this is a great game to buy. There is no game like it so it will not be in direct competition with other titles you may have. The content in the box is more than enough to fully enjoy the game for a long time so there should be no need to add the expansions for a good while yet. I would stress that this is a game best played with either five or six players. A three player game does not have quite the same feel compared to a game with at least five players.
I hope this review has been helpful. If you have any comments add them. If you have any questions about the game I am more than happy to answer them as best as I can.