In addition to the other region pokemon, Poke Radar, and "just breed piles of stuff" methods, there is a new Consecutive Fishing method which appears to significantly increase Shiny occurances but exists only in Generation 6/ Pokemon XY.
It turns out that if you manage to get a chain of consecuctive fishing hooks, it will gradually increase the likelihood of finding a Shiny Pokémon, with the exact figures still to come. The higher the amount of Pokémon hooked, the more likely you get a shiny Pokémon, but as with PokéRadar, this is not a guarantee.
There are a few things that will break this consecutive streak, however. If you move from the spot, the streak is broken. If you pull in the rod too early, the streak is broken. If you don't get a nibble, the streak is broken. With the latter being a possibility, it's logical to have a Pokémon with the ability Suction Cups as your lead in order to increase the likelihood of hooking a Pokémon.
Some more info on fishing streaks is here:
What we know for sure breaks a streak:
-Getting the "Nothing seems to be biting..." message (Random, but the odds are manipulable)
-Getting the "No! You reeled it in too fast!" message (Pressed A too soon)
-Getting the "No! You reeled it in too slow!" message (Pressed A too late)
-Exiting the area in which you're fishing
-Getting into a battle that isn't through fishing
-Exiting the game
The shiny rate seems to increase significantly by this method and reports seem to indicate around 150-200 consecutive catches may grant a shiny. The problem of course is you can only catch shinies that can be fished up in that area, and it's mostly luck as to which pokemon you get (unless you want a shiny lucdisc or Magikarp, in which case use the Old Rod).
200 catches may seem high, but it's miles ahead of the one in 8000+ chance normally and still significantly better than the 1 in 1,365.3 chance the gen 5 foreign Ditto chance had (it is unknown if the foreign ditto method has improved in gen 6 yet).