Well, as I said earlier, Red doesn't have the best limits, but he's got a few good ones.
Sled Fang -
He charges into one enemy for a moderate amount of damage. This is quite
useful in the beginning of the game, when he has no long-range attacks.
(The name of
the limit in the Japanese version was Shred Fang. Sounds cooler to me.)
Lunatic High - He howls, and columns of yellow light erupt from the ground, casting Haste on all party members. Useful for a while, but the Time materia will eventually render it obsolete.
Blood Fang - Similar to Sled Fang, only it drains a small amount of HP and MP from the enemy. I never noticed any really huge boost in his HP or MP, so in my opinion it's not too useful.
Stardust Ray - His howl sends a huge cloud of falling stars down upon the enemies. Once you get this, you shouldn't ever have to use Blood Fang again. This is much more powerful.
Howling Moon - He leaps into the sky, and howls at the moon. When he lands, he is affected by Haste and Berserk. Not the most useful attack, but it works if you need to take out enemies fast.
Earth Rave - My personal favorite. He attacks the enemies five times, hitting a different one every time. Sure, it's no Omnislash, but it does a LOT of damage (9000+) once you get the Limited Moon. And it has a cool name....
Cosmo Memory - The galaxy compresses into a sphere of fire, which blasts all enemies for 9999 damage. I like Earth Rave more, seeing as it can do over 45000 damage to a single enemy, like Safer Sephiroth....hehehehehe...