Autisics stim. If you've ever spent time around autistic people -- especially autistic children -- this is pretty much a given. What most people don't seem to consider is that NTs stim, too.
In fact, there are circumstances under which NTs even use many of the stereotypical autistic stims (or, more technically, "self-stimulatory behaviors") and under which those stims become generally understood -- and even almost expected.
Admittedly, most of those circumstances are pretty extreme, emotionally speaking, but one of the (many) hypotheses floating out there about autism is that it's (at least partially) caused by a deficit in the ability to self-regulate emotions. In many ways, this is an argument which helps support that theory.
On the other hand, there's also evidence against that idea. There are certainly difficulties with emotional self-regulation in autistic individuals -- and even Aspies such as myself -- but issues of causation are complex.
In any case, as I mentioned before, there are certain types of stimming that NTs regularly engage in. Many autistics engage in these same stims as well, but they're not usually pathologized unless there is an issue with the context. For instance, some autistic individuals have been known to masturbate in public because they don't understand why they shouldn't.
While that particular societal more may seem silly when looked at by someone without our cultural baggage, it is rooted in many deep-seated beliefs about sexuality. As such, it is unlikely to change anytime soon.
And yes, masturbation is a type of stimming... or, more accurately, a category of types of stimming. It involves repetitive movement intended to stimulate the senses of the person engaging in it in a specific manner... which is pretty much what the definition of stimming is.
While that particular type of stimming is pretty easy to find among NTs, the stereotypical autistic stims (e.g. rocking, head-hitting/banging, hand-flapping, spinning objects...) are somewhat more difficult to find.
Discounting children's use of rocking horses and adults in rocking chairs, there's one circumstance in which NTs frequently rock. When they're given extremely distressing news (e.g. the death of a loved one), many individuals will have a reaction that's quite familiar to many autistics. Specifically, they will start crying, almost hold themselves, and start to rock back and forth. Despite the extreme circumstances, this rocking serves almost the exact same function as it does in autistics: it's a soothing motion, one that helps the individual cope with an extreme emotion.
In NTs, head-hitting and head-banging is usually reserved for moments of extreme frustration or what I like to refer to as "D'oh!" moments. While NTs usually don't engage in this behavior with the same intensity (or frequency) that many autistics have been known to, that is a quantitative, not qualitative, difference.
Hand-flapping also follows this pattern. If you've ever watched videos of people as they are informed that they won the lottery (or Publisher's Clearinghouse sweepstakes, etc.), you probably know what I mean: many people in such circumstances jump up and down, waving their hands excitedly... in a manner quite familiar to most in the autism and autistic communities.
Finally, object-spinning is mostly a matter of autistic children (which is to say that autistic adults don't do it nearly as much). Parallels in NT children are pathetically easy to find. Simply put, neurotypical chlidren like spinning toys. Autistic kids like to spin toys... including spinning toys.
Edit: Corrected a typographical error.