What do you do with Play Coins?
Solution 1:
For built-in software, they're used in:
- Streetpass Quest I and II: Two coins apiece for a "wanderer", random color, level 1 or 2, that goes along with miis you've met. It's usually a good idea to max out to have 10 characters in the party whenever you "venture forth". In quest 2 you can also spend 2+level coins to have previously met miis rejoin even without meeting them again.
- Streetpass Puzzle: 2 coins get you a random blue piece of any panel that you've started but not yet finished. Note that this may be a piece you already have.
- AR Games: Unlock game modes and other extras.
- Swapnote / Nintendo Letter Box: Pay 5 coins for stationery. (No longer available)
Additionally, any game can use play coins for in-game unlocks. For example, in Street Fighter IV you can use them to get a random figurine; in Kid Icarus: Uprising you can use them for idol toss eggs. In shovel knight, you can pay 1 coin for 100 in-game gold.
Solution 2:
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!
Solution 3:
Additionally to MaHuJa's usages I could use play coins to buy weapons in Raid-mode in Resident Evil: Revelations. I think they were usable in Street Fighter too, but I can't remember properly (and sold the game).
Seems that any 3DS game can use play coins, so it's up to the game-makers to include them.