Must own 3ds titles?

Depends on what you like, but my favorite 3DS games are Fire Emblem Awakening, Bravely Default, Tales of the Abyss, Shin Megami Tensei 4, and A Link Between Worlds.

Pokemon. All the Pokemon games.

Rune Factory 4
Shin Megami Tensei Devil Summoners Soul Hackers
Theatrhythm
Shin Megami Tensei IV
Fire Emblem Awakening
Tales of Abyss
Code of Princess
Bravely Default
Animal Crossing New Leaf

Dunno really. Mario kart, professor Layton, Pokemon (if you're into it). Just a few off the top of my head.

Mighty Switch Force 1 + 2

The entire Phoenix Wright series. OBJECTION all the things!! :D Also, 999 Nine Hours Nine Persons Nine Doors and its sequel Virtue's last Reward :)

Fire Emblem: Awakening. Pokémon X/Y. Phoenix Wright: Ace Attorney - Dual Destinies. The Legend of Zelda: A Link Between Worlds .

Zero Escape: Virtue's Last Reward, a bit better if you've played 999 (as it might be hard to go back to it afterwards, the actual link between games are fairly minimal) but in itself a very awesome game.

solatorobo, ghost trick and the ace attoney games

Retail Games: Super Mario 3D Land, Mario and Luigi Dream Team, Etrian Oddysey Untold/4, Rune Factory 4, Zelda Link Between Worlds, Kid Icarus Uprising, Mario Kart 7, Pokemon X/Y, Animal Crossing New Leaf, Bravely Default, Fire Emblem Awakening, Luigis Mansion Dark Moon, Shin Megami Tensei IV, Resi Revelations, Kingdom Hearts 3D, Theatrhythym Final Fantasy

Debatable Must Own Ports: Ocarina of Time 3D, Star Fox 64 3D, Donkey Kong Country Returns 3D, Tales of the Abyss

Upcoming Must Own: Bravely the Second, Smash Bros 3DS, Final Fantasy Curtain Call, Fantasy Life, Pokemon Alpha Ruby/Omega Sapphire, Persona Q

The retail part of this list was made based on the currently owned libraries of myself, my brother, and my girlfriend.
I own all the ports, but some people don't count those hence the debatable title.
I excluded eshop titles to keep this post shorter than it would have been.
The upcoming list was made off the preorders of the three previously mentioned people.
Obviously this list is based on OPINION, some games (such as Monster Hunter, Professor Layton, Phoenix Wright) were not put on this list because myself, my brother, or my gf have not played them or didn't like them. This does not mean those games are not must own titles to some or most people. Also despite the fact that you asked for all must own titles I don't have the time nor the funding to try out every game which goes back to the previous point about games not being on the list.

Most importantly ENJOY!!!

Thank you all!