For those wanting to grade in Traditional Karate-Do there is a kata assigned to each belt level:
9th Kihon kata
8th Heian Shodan
7th Heian Nidan
6th Heian Sandan
5th Heian Yondan
4th Heian Godan
3rd Tekki Shodan
2nd Bassai Dai
1st kyu Kanku Dai
black belts:
1st dan Jion
2nd Jitte
The kata we practice here is Japanese Shotokan kata.
However we also look at the ShotoKai versions of the kata for a more fuller understanding, and the Okinawan versions of the kata.
The Heians are called Pinan on Okinawa and performed slightly different. The Tekki are called Naihinchi, etc.
Nobody has to learn kata for STMA and I don't teach it in class regularly. It's there for people who want to add the dimension of kata to their training, or for those who want to learn the Traditional karate-Do.
I will sometimes teach a kata move and it's bunkai in class, explaining where it came from, to give students a deeper understanding, but they don't have to learn the whole kata.
In fact, I tend to start with bunkai and work back, so a kata is really a sequence of bunkai. This gives a greater understanding of what you are doing it for.
We also teach the 3 Wing Chun forms:
Sil Lum Tao
Chum Kil
Bil Jee
We also teach the Yang Tai Chi short form.
There will be weapons kata in the future for those who want to add that dimension to their kobudo.
We have kata for each of the Okinawan weapons:
Bo
Nuncha
Tonfa
Kama
Sai
in fact there are several nuncha kata we use.
There are forms for the WC Bart Charm Dao swords and the Kwane "Dragon" Pole, which is very different from Bo.
For the Japanese kobudo, "kata" means something different, so there are no set forms, although there is a Jo "kata" in Aikido worth learning.