Seeing as the Cube has been my only console (unless you count the Atari 2600 many years ago), my choice seems to be restricted. I loved Super Monkey Ball, as much for being so different as for the gameplay, but the best for me has to be
Animal Crossing.
I've got 3 kids, and all of them had characters, along with my missus (this is the only
'computer game' she's ever had any interest in) and myself, and if you added up the hours of gameplay this game had, it would be higher than all the other games added together.
We spent months and months playing this, so much so that we bought another cube to go in one of the kids rooms, just so we could get more hours in