Konnichiwa! After a Friend asked me what Pokémon Game they should get, it occurred to me a lot of people might want to know that. So I'll describe each of them (without spoiling anything major).

X/Y (Gen 6)

The first Games for the 3DS, they have all of the Gen 6 Pokémon in them (between both Games). You can completely Customize your Character, which is AWESOME. You have 4 Friends travelling with you throughout the Game, which is cool. The Storyline is good, but also pretty long (by the time you're ready to enter the Hall of Fame, you'll be fighting Trainers with Pokémon around Level 70). Also has some cool new features, such as PR Videos, Roller Skating, Riding Pokémon, and the Friend Safari, just to name a few.

Ω Ruby/α Sapphire (Gen 6)

IMO The Best Pokémon Games Ever Made! (HG/SS being a very close second.) It has a whole New Story, New Characters (including my favorite: Zinnia), New Mega Evolutions (compared to X/Y), and also lots of nostalgic moments for players of the original Gen 3 Versions. It has a TON of Legendaries, many cool new features (such as Soaring, and the DexNav), and also post-Hall of Fame Move Tutors, like in many older Games. Also, if you're missing Pokémon from older Games (especially Starters), these Games have plenty.

Sun/Moon (Gen 7)

Definitely the most original Pokémon Games ever made (as part of the Main Series, anyway), if you're looking for something different, this is it. There's lots of things you'll have to get used to, though. There are no HM Moves, nor any Pokémon Gyms. Instead, you have special Ride Pokémon that replace HM Moves (as well as certain items, like the Dowsing Machine, and the Bicycle), and instead of Gyms there are Trials, where you face VERY POWERFUL Wild Pokémon. Additionally, there are lots of new Pokémon, including "Regional Variants" of lots of Gen 1 Pokémon. The Storyline is pretty neat, too (very sci-fi). There's lots of new features, including the return of Character Customization, Festival Plaza (a cross between the PSS and Join Avenue), Poké Pelago (a place where you can have Pokémon do things like Dig for Treasure, Train their Stats, and more), and the RotomDex (which is AWESOME).

Ultra Sun/Ultra Moon (Gen 7)

Eveything I said about Sun/Moon pretty much applies to these Games, too. They changed the Storyline dramatically, added a few new Legendary Pokémon (and a TON of older ones), some new Z-Moves, and added what's quite possibly the hardest battle in any Pokémon Game, as a part of the pre-Hall of Fame Story. There are also Move Tutors now, and a few new Features (like the Photo Studio, Mantine Surfing, and the Battle Agency). There's also some new Outfits, including my favorite outfit of any Pokémon Game (the one in the picture at the top of this section).

Conclusion:
If you're looking for a Game that is Completely New, has Character Customization, and yet is still a traditional Pokémon Game, X/Y is the way to go.

If you like older Pokémon Games (the Games these are based off of, in particular), or if you like being able to do things like Dive Undewater, and have your own Secret Base, then I'd recommend Ω Ruby/α Sapphire.

If you want something that's different than normal (or simply want the latest Game, with the most Pokémon in it), then Ultra Sun/Ultra Moon is best.

If anyone has any questions, or if I left something important out, please leave a comment. Sayonara!