For this keep watching the app store for the Free app of the week.
There are quite often good apps / games for free that you would have had to pay for.
Another not so free option is to go to your local Starbucks and grab whatever they have out for free... though it is tending towards being music again. (no so free as they would like you to buy a coffee to grab that
Most of my favourites on my phone are no longer listed on the app store.
Also you have the usuals from Zynga and King (Bubble Safari, Bubble Witch, Candy Crush, Farm Heroes, etc.)