[bamboo]

Here is the basic breakdown.

OLD SCHOOL

Aiki-Budo
Name given to the art O sensei taughtbefore it became known as aikido. It is very close in style to Daito-ryu Aikijujutsu. It is considered to be one of the harder forms of Aikido.
Shin'ei Taido
Founded by Noriaki Inoue. Not officially aikido as the founder of this art claimed it was the same but "different" He studied under O sensei
.
Yoshinkan
Gozo Shioda style. Shioda sensei studied with O sensei from the mid-30s. This is considered the hardest of of the aikido schools and is still used by Tokyo police to this day

Yoseikan
Formed by Minoru Mochizuki, early student of O sensei and also of Kano-sensei at the Kodokan. This style includes elements of Karate and Judo, also called "Yoseikan Budo"

NEW SCHOOL

Aikikai
This is the mainline branch of aikido as headed by the third doshu, the founders grandson son. This is the Ueshiba family organization. Has groups in N. America like USAF and CAF.

Iwama-ryu
While still a part of the Aikikai, the style taught by the late Morihiro Saito. Saito sensei wanted to preserve aikido from the early 50's as to taught to him in Iwama.

Nippon Kan
Founded by Gaku Homma,VERY traditional school..

Aikido Schools of Ueshiba (My school and "style")
Heaaded by Mitsugi Saotome. Saotome sensei has an eclectic approach to teaching Aikido, we learn everything from hard practical techniques through to soft abstract sensitivity exercises. We do tons of weapons under him. Was independent for years and rejoined aikikai organization, but style is dissimilar enough to warrant mention.

SPORT AIKIDO

Tomiki-ryu
Founded by Kenji Tomiki, Tomiki didn't do ki and believed that aikido should be sporting and competitive along the lines of judo. Lots of rubber knife and kata type competition.

Jiyushinkai
Off shoot of tomiki.
Fugakukai
An off-shoot of Tomiki-ryu founded Karl Geis.
NO competitions


KI styled schools ? as originally split by Tohei Sensei

Shin-shin Toitsu Aikido
Founded byKoichi Tohei - Aikido with Mind and Body Unified. This is ki development and as far from the martial aikido as you can get. Practitioners look like they are dancing or even skipping from time to time.

Shin Budo Kai
This style is headed by Shizuo Imaizumi

Kokikai
Founded by Shuji Maruyama. He was a chief instructor with the ki society but split to form his own ki group. More weapons and technique here than with Tohie's group.

Seidokan
Founded by R. Kobayashi. Another Ki split

(I'm sure there are more but I don't think its worth getting into as they independent groups doing Ki aikido)

There are more but these are the main ones.

-bamboo