Answer: Giardia duodenalis (a.k.a. G. lamblia, G. intestinalis) trophozoites with "falling leaf" or "tumbling" motility. Note that this is quite different than the "spiraling" motility of Chilomastix mesnili and the "jerky" motility of Pentatrichomonas hominis - two other flagellates - both non-pathogns - that may be seen in human stool specimens. As pointed out by Florida Fan, the motility is further enhanced by dark field videography, which makes everything more interesting. Thanks again to Idzi for the very cool videos!
Santiago gave us further information on how Giardia trophozoites move in the intestine to attach to the duodenal intestinal mucosa:
After excystation in the small intestine, the trophozoites quickly swim towards the epithelium and attach forming a monolayer; this contributes to the pathology and allows the parasite to escape the turbulent flow of the small intestine and continue the life cycle in the human host.
To achieve this, it uses a combination of movements involving its four pairs of flagella as well as its caudal region, and it is able to switch its motility from "free swimming" in the intestinal lumen, which is more rapid, to a "pre-attachment" pace which is slower and more stable, facilitating effective attachment to the intestinal epithelium in the desired location to form a monolayer.
Lastly, Old One reminds us how
Antonie van Leeuwenhoek was delighted when he took a look
at his own watery stool
Seeing For the very first time
“Bellies flatlike with bodies furnisht with sundry little paws. making quick motion with these paws, yet for all that, they made but slow progress yet a-moving very prettily.”
What a neat parasite!