Let's look at today's roster of popular Dragons…
Garchomp was deadly yesterday, is deadly today, and will be deadly tomorrow. The intruduction of the Fairy has barely made a dent the the ol' dragon-shark, as can be plainly seen in the sheer power of his Earthquakes that make Fairies run and hide under their beds.
MegaMence was quickbanned at the very start of Gen VI. It had the ability to tank some of the weaker Fairy attacks, set up a Dragon Dance, then slay all of the Fairies bar Clefable with Return. Please not that no Fairy has ever been quickbanned to Ubers, and that Mawile's ban is still being debated.
The Lati twins have seen no less use now as they did in previous gens. Latios still does his thing – wreck everything with Life Orb Psyshock – and Latias is still that bulky attacker you all know and love. Fairies haven't scared these Dragons one bit.
Takes neutral damage from Fairy attacks, tanks Moonblasts from Xerneas all day and KOs with Flash Cannon. Dialga is a Fairy's worst nightmare.
Mega Charizard X
Fairy is not very effective against Fire. MegaZard X is Fire/Dragon. Therefore, no Fairy weakness. While he still doesn't like Fairies, he's still an A-rank threat and doesn't flinch in the face of magic.
Heck yeah. Screw Fairies, I'm a fluffy cloud dragon that's also a pixie. Heck yeah. I don't give a crap about those Fairies because I am proof that you can have the best of both worlds. Heck yeah.
If you've ever been wrecked by a Weakness Policy Dragonite then you know what pain is. Dragonite posesses a deadly physical and mixed set, and has a terrific variety of moves. Multiscale makes him an absolut monster to take down, and imagine an Iron Head from a +2 Dragonite after he survives a Moonblast. Ouch.
Too strong for Ubers, had to have another tier made just for him. Take that, Sylveon.
In conclusion, the Dragon-type has suffered a blow from the Fairy-type, but there are still those who defy Game Freak and keep on wreckin'.