Ok, so here are all of the possible ways of using Play Coins on the 3DS (That I know of):
Find Mii I and II. Play Coins are used to hire random heroes and "Old Allies" (enables you to hire people you have tagged before.)
Puzzle Swap. Play Coins can be used to buy puzzle pieces. You cannot buy a pink piece (puzzle pieces that can only be obtained through streetpass) with Play Coins.
Mii Force. Play Coins can be used to hire troops for your missions through the galaxy. You can buy a troop with a random-colored shirt for 2 Play Coins, or you can buy a troop that you have played with for 3 Play Coins each.
Flower Town. Play Coins can be used to invite guests to help your plants grow.
Warrior's Way. Play Coins can be spent hiring an army. The number of troops in an army increases as you fortify your castle. You can fortify your castle by defeating another army with building supplies.
- Monster Manor. Play Coins can be used to hire investigators. Each investigator costs 2 Play Coins.
Pokémon Dream Radar. Play Coins can be used to get Dream Clouds.
Animal Crossing: New Leaf. A player can buy a fortune cookie from the Nookling Junction (or all its other upgraded forms) for a "modest" 2 Play Coins.
- Swapnote/Nintendo Letter Box. You can use Play Coins to buy unlocked stationary and unlock certain features (such as the ability to attach recordings or photos to your notes).
(EDIT: As of Thursday, October 31, 2013, Swapnote will no longer be in service. It will not be in service due to inappropriate notes being sent to minors. So, buying stationary would be useless, because you cannot send any notes via Spotpass no more.)
I hope this information helped!