What game do you like most?
You are asking a person, of all the games in the world, for the one he likes most.
Which game do you like most?
The person may have said, "I play tennis, polo and golf." You use 'which' here to ask him, because you are asking him to make a choice from those three.
Use 'which' when you are asking for information, and you are asking the person to pick out one or more things from a definite number of specified things or people etc.
'What's your favourite food?"
but, if you offer a box of chocolates with soft and hard centres,
"Which one would you like?"