As stated in the title, you can choose any game (to my knowledge) to checkout and purchase for free. You will need to have a Big Fish account as well as an external Big Fish Games application manager to play these games, however they're completely free.
If you untick the 'Big Fish Game Club Free Trial', you will not need to give your credit card details. Enjoy!
Personal favourites: I particularly enjoy the Nancy Drew games, however I also like the hidden object games (though those can get a bit repetitive).
Found another free code! Use FREEGAME907223 if you haven't already :D
Also, most likely to be only for PC +/- Mac (don't have Mac to confirm, however am happy to be corrected.