For example here are a few walk, march and run cycles of some well known hand drawn characters which I have taken from http://www.donbluthanimation.com/_Don_Bluth_Animation_Cyber_Garage_Project_march_run_cycles.html
Listening back to the link on my previous cycle post from Cable Harding he states
Scooby Doo is a prime example of cycles used in cartoons, a lot of this is heavily reliant on the story line as a lot of the time Scooby and the gang find themselves running away from monsters or chasing them instead. This allows the makers at Warner Brother to take advantage of cycling a series of frames saving time and resources.The character will stay in the middle of the frame meanwhile the background will move behind it, it's kind of like Scooby Doo when the mystery machine stayed in the middle of the screen and the back ground moved behind it.
Here are some examples:
1:00 stairs, 1:45 crocodile
0:15 eyes, 1:02 stairs, 1:16 chase, 1:50 bookshelf, 2:47 tightrope
A musical parody but it has some good examples of cycles, one of which is the mystery machine cycle with the moving background
scooby and scrappy intro
It's safe to say that there are a LOT of examples in the Scooby Doo cartoons!
Equally I have looked at the Fleischer brother films which due to a similar style to Scooby Doo include a lot of cycles within their work. I came across my first example from the John K blog with an example of Betty Boop http://johnkstuff.blogspot.com/search/label/cycles.
Here are some good Fleischer cycle links:
Nice cycle sequence at 5:43
Cycle sequence at the beginning with example of background movement, walrus
walk sequence at the beginning and spaceship
Good cycle at the beginning with kids on the shoe
These are just examples of two different cartoons, there are many examples out there maintaining the same style and technique with the use of cycles in hand drawn animation.
Looking outside of hand drawn an obvious one to use would be one which we have been shown in Visual Culture created by print work, feet of song.
Similar to hand drawn CG Animation can easily create things such as run and walk cycles, it is stop motion which I have found hard to research.
Here are some examples of walk cycles created using stop motion:
However they don't have the obvious cycle quality that hand drawn purveys as Stop motion as a technique is destructive animation and therefore you can not repeat the same thing twice, you can only try to make it look the same.
Looking at some well known films I have come across what are cycles but they don't look the same, they just repeat themselves:
Wallace and Gromit - counting sheep
Coraline - circus mice
I don't think cycles are limited to hand drawn pieces completely but they can't be true cycles outside of this technique.