First, in defence of chess it is a great game and I personally enjoy it and spent a lot of money on a good quality board and pieces. However even if you allowed for chess as an answer, it wouldn't be my favourite and out of the "traditional" games, that honour would fall to the far deeper WeiQi (go).
However, assuming that Go is also off the list and you are looking for more modern games, that is a tough call. My most played board game is probably Midnight Party by Ravensburger, partially because that is a game I can play with children or adults and there is depth enough for the adults and simplicity for the children.
In terms of favourite game to play, that might be a bit more difficult. In terms of mainstream games, the honour would fall to Risk but when you open the field up a little, then Starfarers of Catan, Carcassonne or Zombies!!! would probably be the three from which I would choose.
Honourable mentions should also go to Canyon, Settlers of Catan, Ave Caesar and Betrayal at House on the Hill.