There are a number of 1 person Ken no Kata. Here is one example.

Movie of the kata.

See below for a printer friendly description of this kata.

Walk to the centre of the mat, facing the sensei, kneel into seiza and perform a rei.	Step up onto your right foot (left knee on the ground), drawing your sword …	… as if cutting an opponent horizontally across the stomach.
Stand upright, feet together, turning the sword to prepare for a downward diagonal strike, bringing your left hand to also grip the sword.	Step your right foot forward and bring the sword across your body in a downward diagonal motion, …	… as if cutting an opponent from collarbone to hip.
Step your right foot back and bring the sword across your body …	… as if cutting an opponent horizontally across the stomach, once again …	... contd.
Slide your left foot back to bring your feet square, bringing the sword across your body and up into the guard position, holding the sword with your right hand only.	Bring the sword down across the front of your body in a swift motion - to shake off the blood.	Re-sheath the sword…
… contd …	… contd …	… contd …
Kneel and rei.

There are a number of 1 person Ken no Kata. Here is one example.

Album with photos/movie of the kata.

Album with photos and movies of the kata.

See below for a pdf version for offline viewing and improved printing.

This kata is a relatively modern kata, having been created in 1956. It consists of 21 techniques against an unarmed as well as armed attacker. It is divided into 2 unarmed sets and 3 sets with weapons. The first 7 techniques are against an attack close in. The next five are against attacks from strikes and kicks. Then there are three attacks with a knife, three with a stick and three with a gun. While the actions are controlled, so that the attacker is not hurt, the defender's actions can easily be modified to disable the attacker. It is important to realize that all of the techniques in this kata are consistent with the principle of "jiu", the principle of gentleness or yielding.

This 2-person kata consists of uses the bo to defend and attack.

Tori (on the right of the sensei) and uke (on the left) stand facing each other at the edge of the mat. The bo is held vertically in the right hand with the bo in front of the arm (about 2/3 down the bo with the thumb down and palm facing forward). Both turn to face sensei and rei, then face each other and rei. Each take a step forward with their left leg, then a step to their right. Both walk forward leading with their left leg until approx 6’ apart. With feet together, the bo is then transferred to the front of the body (thumb up) and swept up to be held in both hands (right palm up, left palm down). At the same time each step to the left into a deep kiba-dachi to end up facing each other.

The kata ends with a reverse of the beginning steps.

Glossary:
• kiba-dachi = horse stance
• zenkutsu-dachi = forward stance
• yoi = guard stance (there are forward and reverse versions in this kata)