The Denpa Men: They Came by Wave is currently my favorite e-shop game. I have tried explaining the game to a couple friends and the best description I can come up with is "Pokémon x Dragon Quest."
The premise of the game is pretty simple: you capture "Denpa Men" in a style exactly like that of Pokémon Dream Radar. Every time the 3DS picks up a wireless signal (it does not have to actually connect to the signal), three Denpa Men appear in the tower. All you have to do to capture them is hit them with a net by pressing A.
Each Denpa Man has a color (type) and the possibility to have an antenna (special skill: heal/attack/buff/debuff/etc.). Like Pokémon, there is a type chart: each elemental attack is weak against certain colors and strong against certain colors. Some of these attacks have strangely Pokémon-esque names (Water Gun, Flame Thrower), which isn't much of a surprise considering the studio that made the game is none other than Genius Sonority.
You begin with a party of four Denpa Men, but as you progress through the game your party size increases to 8. There are a number of dungeons with randomly spawning enemies that you must pass through in order to progress in the game. The battle system is essentially a simplified version of the battle systems you are familiar with from games such as Dragon Quest and Final Fantasy. You have the ability to perform a basic attack, the ability to perform a special attack (requires AP), and the ability to use an item. To ease your quest, you have the ability to equip Denpa Men with certain armor that changes basic attack type, increases elemental resistance, boosts stats, etc. The number of possible Denpa Men and the ability to customize them increases the variety present in the game a hundredfold. Antenna Powers have the possibility to "power up" as you gain levels and level-based stat boosts are completely unique to a specific Denpa Man. One of the best features of the game is the ability to share your Denpa Men with friends via QR codes. Your friend simply has to progress far enough in the game to unlock the PC, scan the QR code, and allow the Denpa Man to join the team. Unfortunately, the new Denpa Men start at level 1; however, this is assuaged by the fact that all Denpa Men, even those in the "room" (think Pokémon PC box), gain EXP at an equal rate to those in the party--essentially a universal EXP Share.
Here are a few screenshots if you are interested. You can download the demo for free in the e-shop.
And here is a picture I took of my team in the second dungeon; it gives you a slightly better view of the battle system/screen.
I'm currently around level 22 and in the fifth dungeon. I'd love to share QR codes with Smogonites. Pick up the game!