League of Legends (LoL) Question: Ultimate

Akali has a really short cooldown on her ultimate, Shadow Dance has a very short cooldown, she gets 1 stack every 30/22.5/15 seconds, and can hold 3 stacks.

Kassadin, Anivia, Diana have really short cooldowns on ulti. (With exception of the form switchers and udyr)

I'm not quite sure what you're asking. Are you looking for champions that can cast their ultimates very frequently? Lux and Kayle have pretty low cooldowns on their ults, which allows them to cast it in pretty much every fight late game.

Udyr doesn't have a real ultimate. Instead he has 4 basic abilities and each of them can reach up to 6 ranks.

Jayce can also reach 6 points in his basic abilities while his ultimate (which switches him from melee to ranged form and back) is available at level 1.

Other form-switchers like Nidalee and Elise can put points into their ults, but they can also switch forms at level 1.

Karma also has her ultimate at level 1. Mantra empowers her next basic ability and has a pretty low cooldown which gets lower when you attack enemy champions.

I hope that answers your question. If you're still wondering something, please reply with more details on your question.