P - Kyo is a great groove for Kyo. He has a great hop so he can crossup people on the ground. His standing HK is beyond ridiculous. It comes out fast, punishes low attacks, has good priority, and can even link his level 3 Serpent Wave off of it. Kyo is all about playing footsies and spacing with standing HK, and when you're able to get inside, being able to connect his Wicked Chew combo off of his multitude of low jabs and medium. His jumping lk is a good crossup, as well.
On Xbox, P Kyo is good because of the ability to parry and super cancel. When you're constantly landing his standing HK on people, they tend to get stupid and try to close the space in between you two with mindless jumpins, fireballs, or what have you. This is where you're able to parry, counter, and keep the distance away from you again. Good strategy in this case would be to parry a jump in attack, then immediately do a c.lp, c.lk, s.mp xx Wicked Chew. Great damage, good stun, and sends them to the other side. If you have a super stocked, you can just super cancel the second hit of Wicked Chew into Serpent Wave or Final Showdown.
K Geese is another scary SNK character because of his ability to counter, take no damage, but fill a large chunk of his K groove bar. He needs run because his dash sucks and his c.lp is a great pressure string starter. If you can pressure people well enough, then they come at you and you can counter, really making them think it's unsafe to attack you. So what's the safe way to attack Geese? Fireball. What does K-Geese have? Just Defend. Nullifies everything. Unless you're Zangief. Zangief is the only person that can really give Geese any problem, but even he will be afraid to attack a raged Geese. Being able to A-A with Raging Storm or land Deadly Rave from his s.hp or at the end of any of his strings (you can even end Deadly Rave with s.hp xx Shadow Smasher for more damage), this makes Geese a viable character to use in competition.
Other good characters are: Rock, Nakoruru, Yamazaki, Rugal, and Mai in various different grooves.