If you enjoy the Pokémon series and its monster collecting and battling, you might want to look into the various Shin Megami Tensei games available on the 3DS. They're somewhat similar in that you collect "monsters" and battle with them, but rather than creatures and items like in Pokémon, in SMT they're mythological beings, angels and demons. The games are usually set during or after apocalyptic events and there are different routes you can play in a majority of them so there's a lot of replay value.
Gameplay is usually your protagonist and up to three demons in your active party (series catchall term for all of the "monsters", regardless of if they're something like angels) against whatever opponent(s) you encounter. You can recruit non-boss enemies by talking to and negotiating with them, and you fuse demons to make stronger ones so you don't really want to get attached to particular ones. A lot of the games feature the Press Turn System, wherein you exploit enemy weaknesses to gain extra turns to take more actions, whether you want to keep attacking, defend, heal, use an item, whatever. You, your demons, and enemy demons all have unique weaknesses. This means that while you can exploit the enemy weaknesses, they can also exploit you and/or your demons' weaknesses to give themselves more turns as well. It's quite fun.
Shin Megami Tensei IV is probably the best to start with as far as these 3DS games go. Most accessible in terms of gameplay, cool story, great music and generally the best representation of the series overall to a newcomer to be found on the 3DS, I'd think.
Shin Megami Tensei IV Apocalypse is an alternate story set in the middle of Shin Megami Tensei IV's Neutral route, so you shouldn't play it until you've played the original Shin Megami Tensei IV. The tone tends to rub people the wrong way because it strays a bit from normal SMT in some aspects, but the gameplay is good.
Shin Megami Tensei: Strange Journey Redux is available as well. The original Shin Megami Tensei: Strange Journey on the DS is regarded as better tonally, but it's also a bit expensive and hard to find, so it's a toss-up. This one is more like classic Shin Megami Tensei games in that it's a first-person dungeon crawler, so you'd have to be open to that sort of gameplay. It's great though and worth it if you're open to that.
If you enjoy turn-based tactics games like Fire Emblem and those sorts of games, Shin Megami Tensei also has those in the form of the Devil Survivor games. Devil Survivor: Overclocked is an enhanced port of the original Devil Survivor for the DS and it adds more demons and extra endings and is worth playing over the original. Devil Survivor 2: Record Breaker is not a sequel and can be played on its own, but like SMT IV: Apocalypse, it's a bit different in tone than the other SMT games. I'd say both are worth checking out but I favor Devil Survivor: Overclocked. There are a bunch of endings to choose from, more than usual games, since each character you can have in your party has their own route. Lots of replay value and they have New Game+ perks to make it less daunting a task to replay them.
Finally, there's Shin Megami Tensei Devil Summoner: Soul Hackers. It's a first-person dungeon crawler like Strange Journey. Fun 90s cyberpunky sort of setting since it originally came out in 1997 for the Sega Saturn, then ported in 1999 to the Playstation, then the 3DS in 2012.
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Since I mentioned Pokémon, all of those mainline games were fun.
X & Y were the weakest because they're easier, but still had fun aspects like introducing trainer customization, letting you work at a hotel to earn money to afford all those clothes, Super Training (a quick and easy way to EV train and earn items), and Mega Evolution.
Omega Ruby and Alpha Sapphire are my favorites on the 3DS because they offer a bit more challenge than X & Y, feature more new Mega Evolutions, let you encounter and catch legendaries from the previous games via portals, create a Secret Base and visit other peoples' Secret Bases, and participate in Contests. They take what X &Y offered and improved on it, and the only thing missing is unfortunately trainer customization.
Gen 7 is tricky. Sun & Moon have the better story, but Ultra Sun & Ultra Moon are the better games when it comes to gameplay, offer more challenge, and have more content and new Ultra Beasts to catch. I lean more toward USUM myself. Also, trainer customization returned, so that was cool.
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Finally, to round out this monster collection-themed post, I'll also second Seastar's suggestion of the Yo-Kai Watch series. I never really gave it a chance for years because it looked a bit too childish, but I got into the series earlier this year since the eShop is shutting down and I figured I ought to grab whatever stuff I was interested in before then. Fun gameplay, neat yokai, worth checking out.
This post got pretty long and was all monster collection related, so I'll probably swing by with a more general list at a later point.
