My favorite abilities thus far have to be Overconfidence (also known as "EarthquakeSpiral" on the site) and Encourage. Both of those abilities look so incredibly useful, and I hope that Encourage negates the negative 2ndary effects of attacks, so that Hihidaruma can use Overheat without sharply lowering it's Sp. Atk, and so Wargle can use Brave Bird without recoil.
Pigeon Heart is also interesting to me.
I'm hoping that Herbivore goes to more than Shikijika (I expect it to, but anyway). It feels sort of useless on a Grass-type, because it's unlikely that anyone (save for the wild Pokemon and "dumber" Trainers) will use a Grass-type move on a part Grass-type Pokemon.
I'd like to see Herbivore on a Water-type or something.
As for the attacks, I'm really liking Claw Sharpen, Sweep Slap, Wild Bolt, Night Burst, Shell Blade, Grass Mixer, Nitro Charge, Drill Liner, Grass Oath, Fire Oath, Windstorm, and Acrobat.
I'm especially excited for:
Wild Bolt - It looks like it could be like Volt Tackle, but easier to distribute to Pokemon like Luxray!
Sweep Slap - I just like it. I love Chillarmy.
Grass Oath and Fire Oath - What do these moves do? Perhaps they raise Grass/Fire attacks respectively. I expect a 'Water Oath' as well.
Acrobat - so interesting and very useful for the new Triple Battles. I think it'd be cool if it could attack the other Pokemon in Rotation Battles, but it's effects as of now are good.