Regenerator, No Guard, Pranskter and Technician are some of the best ones.
Regenerator lets you regain one third of your health every time you switch out. This is very useful on Tornadus-T, who takes no damage from Stealth Rock (Technically) if he switches out immediately after coming in. No Pokemon would complain about having it.
No Guard lets any move hit without ever missing. While this also makes the opponent's move never miss, it also lets DynamicPunch and Stone Edge to never miss. Golurk is a nice abuser of this, as it gets DynamicPunch and doesn't take much damage from Stone Edge.
Prankster lets any non-attacking move to go first. It can transform a horrendous Pokemon into something very viable, and especially annoying. Sableye is a prime example of that. It has horrible stats, although it's in UU because it has access to Prankster Will-O-Wisp and Taunt, which can screw up any Physical attackers / set-up sweepers, Baton Pass chains, etc.
Technician is one of the best abilities in Pokemon, simply because it power up any move under 60. Pokemon like Breloom adore this, as they can spam pretty damn powerful priority in Mach Punch, and Bullet Seed. Scyther and Scizor also like it because they get Bug Bite, Bullet Punch, etc. I especially like using Fighting Gem Breloom because it's Mach Punch just hits so hard when the Gem activates.
Magic Guard basically protects your Pokemon from any real damage outside of attacks. So my Alakazam has Magic guard. I can freely use it in hail or sand without a worry of taking damage. It also negates the loss of Hp from life orb and is a nice ability to absorbs Toxics. Entery hazards also do not damage the user.
Huge Power is an awesome ability, though only a selected few receive this amazing ability. It doubles the Atk of the Pokemon. That's great so if my Azuramaril had Huge Power its base 50 attack would become 100 base attack right? that's 328 Atk at max investment. Well no. It doubles the attack of the Pokemon (not linked to base stats). So this means at max attack Azuramarils atk is not 219, not 328 but 438. That is the same as Groudons (or any base 150 atk Pokemon).
Adaptability Is a nice simple ability that increase the damage your stab attacks do by 1.5. So if my Porygon-Z used tri attack vs a neutral Porygon the damage would be the equivalent to 2x damage basically. That's like basically making a neutral move become super effective. So good.
Weather Abusing abilities (Speed)
Chlorophyll, Sand Rush and Swift Swim double the speed of the Pokemon in its respective weather. Not only does it make the Pokemon a good revenge killer but also a very threatening sweeper capable of sweeping your whole team if you don't have a way to stop it.
