The literature on social grooming in humans mentions
examples of grooming, most of which are unique to humans, include: running fingers through another’s hair, giving massages, washing the body or hair, shaving, removing lint or hair from another’s clothing, swatting away insects, and giving manicures or pedicures, and removing pus from blemishes or wounds. Grooming for humans can also include applying something to the skin or body as with lotion, nail polish, or make-up.
However, probably the more prominent and interesting line of research in this regard concerns language. The foundational BBS article by Dunbar (1993) argues that
Group size covaries with relative neocortical volume in nonhuman primates. This regression equation predicts a group size for modern humans very similar to that for hunter-gatherer and traditional horticulturalist societies. Similar group sizes are found in other contemporary and historical societies. Nonhuman primates maintain group cohesion through social grooming; among the Old World monkeys and apes, social grooming time is linearly related to group size. Maintaining stability of human-sized groups by grooming alone would make intolerable time demands. It is therefore suggested (1) that the evolution of large groups in the human lineage depended on developing a more efficient method for time-sharing the processes of social bonding and (2) that language uniquely fulfills this requirement. Data on the size of conversational and other small interacting groups of humans accord with the predicted relative efficiency of conversation compared to grooming as a bonding process. In human conversations about 60% of time is spent gossiping about relationships and personal experiences. Language may accordingly have evolved to allow individuals to learn about the behavioural characteristics of other group members more rapidly than was feasible by direct observation alone.
In short, under Dunbar's proposal, because human groups are so large and complex, if we were to use the regular, manual grooming of our relatives, we would have to spend around half (e.g. 42% in Dunbar 1993) of our time grooming, which is entirely unsustainable. Language is instead used (and evolved) to more economically fulfill that role. Linguistic gestures, especially small talk, largely overtake the role of manual grooming in humans.
Make of this what you will, it's certainly an important and interesting proposal.