Depends on the game. Some games are free downloads, but cost money to activate and play. Other games are free downloads AND free plays, but will require you to pay money to 'unlock' bigger parts of the game and/or extras. Some games even require you to physically buy it (and get an activation key), then download the biggest part from the internet to be able to play.
Don't ask yourself 'Is it free? Then it is probably illegal.' but 'Is it free? Are other people paying for the same thing as I am? Then it is probably illegal.'