Well, maybe not all rodents; I’m thinking of squirrels, but I’ve certainly seen other types do the same thing. You know: they move for a second, they stop and stand stock still, repeat et al. Why don’t they move smoothly like most other animals?
They seem to move smoothly when the dogs chase them around the back yard! Fast too!
Perhaps they move, then stop to check their surrounding area for danger before moving again? Would you think it might be harder to spot movement if you were moving too?
You’re right, squirrels almost always move by little hops, or else a dead run. But I actually saw a squirrel walk once; maybe it was tired or something? It was one of the funniest things I’ve ever seen. It just put one little leg in front of the other…
I’ve seen them walk like that too!
At my alma mater, they used to walk right up to you in the park… they had had so much human interaction, they seemed to have lost the need to be so nervous. (I think they look much like a miniature bear when they walk, BTW.= hilarious!)
They’d walk around and be very lazy ------> let you sneak right up on 'em. Maybe it’s because we fed them so much that they couldn’t move so fast anymore.
One time, I even saw one sitting on its ass under a trash can with an apple core between its legs taking huge bites. It was holding on with those little arms… it was SO funny. The little bastard just watched people passing along right next to him on the sidewalk - not a care in the world.
Ahhh how I long to be a squirrel…
The reason is that motion attracts predators. You move, then freeze and check out your surroundings. If things seem safe, you move some more, then freeze.
It is a lot easier to see a moving animal than a still one, and this motion style exploits that.
This makes sense up to a point. However, it’s not like the animal is sitting still for several seconds or minutes. It’s more like - move for a half second, sit still for a second, rinse, lather, repeat. Any predator would almost certainly be able to notice the movement.
I have a couple funny squirrel stories,
I was walking on the U-Dub campus crinkling the cellophane from my cigarettes in my hand. I noticed an immediate response from the half dozen squirrels in my close proximity, whether they thought it was food or some wierd mating gesture, I know not. Their ears perked and they bolted in my direction. Soon they were leaping at my calves with wild, determined, squirrel faces. Their little claws piercing my courdoroy. I freaked out and ran, it was way too bizzare. I came back the park the next day with my girl friend to show off my new trick but the squirrels weren’t having it. Foiled!
Another time I was hanging out with my buddy on my back deck, he had a bag of mixed nuts and had gotten the squirrel to eat from his hand. Well, it was summer and I had my chili pepper plant out in the sun. I opened a pepper and rubbed a cashew on pepper skin, not alot, wouldn’t want to kill the little guy. I beckoned the squirrel, who took the nut and stuffed it into his already bulging cheeks. The next second, the squirrel spit out his cache of nuts and was dragging his lip across my deck. Probably the hardest I ever laughed at a squirrel’s expense. Sorry little buddy.
Please don’t call P.E.T.A. on me. 
Last week I saw a squirrel cross a street near my apartment. There were no cars nearby, but the little guy got halfway across, at the yellow lines, stopped for a moment to check if the other lane was clear, and then made the sprint for the curb.
I don’t know if it was just a regularly scheduled stop-and-look, but it sure seemed like he knew that the yellow line was safe, and the cars wouldn’t squish him there.
My guess is just that the loping gait is most comfortable to the physiology of the squirrel. Squirrels really don’t have anywhere they need to be and so it makes sense to just lope along a little, stop, check out the surroundings ( a good idea when in nature a lot of things want to eat you), lope some more and repeat. Rabbits do the same thing and really have about two moving speeds: hop and pause or dead run. “Walking” doesn’t sound like something either would do unless they were near exhausted and needed to keep moving for some reason.