What hormones stimulate non-sexual intimate behaviour? From wikipedia article sexual motivation and hormones, it is said that testosterone/estrogen, oxytocin and vasopressin are stimulating sexual behaviour. But I'm wondering if any of these hormones are linked with physically intimate non-sexual behaviour, like hugs, kisses and cuddles. Also, is there any link through them with having pleasure from these activities?

Is there any research on that and are there gender (sex?) differences?
But I'm wondering if any of these hormones are linked with physically intimate non-sexual behaviour, like hugs, kisses and cuddles.

Kissing is a little messy because it could be characterised as sexual behaviour.
However, oxytocin does has a far more broader role in pro-social and affiliative behaviour than just sexual activity.
Here's one reference. It also seems to suggest a stronger role of oxytocin in women than males:

Effects of Partner Support on Resting Oxytocin, Cortisol, Norepinephrine, and Blood Pressure Before and After Warm Partner Contact
Objective: We examined whether the magnitude of plasma oxytocin (OT), norepinephrine (NE), cortisol, and blood pressure (BP) responses before and after a brief episode of warm contact (WC) with the spouse/partner may be related to the strength of perceived partner support.
Methods: Subjects were 38 cohabiting couples (38 men, 38 women) aged 20 to 49 years. All underwent 10 minutes of resting baseline alone, 10 minutes of WC together with their partner, and 10 minutes of postcontact rest alone.
Results: Greater partner support (based on self-report) was related to higher plasma oxytocin in men and women across the protocol before and after WC. In women, higher partner support was correlated with lower systolic blood pressure (SBP) during solitary rest after WC but not before. Also, higher OT in women was linked to lower BP at baseline and to lower NE at all 4 measurements.
Conclusion: Greater partner support is linked to higher OT for both men and women; however, the importance of OT and its potentially cardioprotective effects on sympathetic activity and BP may be greater for women.
ABP = ambulatory blood pressure; BMI = body mass index; BP = blood pressure; CVD = cardiovascular disease; DBP = diastolic blood pressure; HPA = hypothalamic–pituitary–adrenal; HR = heart rate; IV = intravenous; MI = myocardial infarction; NE = norepinephrine; OT = oxytocin; SBP = systolic blood pressure; SNS = sympathetic nervous system; SRI = Social Relationships Index; WC = warm contact.

And another:

More frequent partner hugs and higher oxytocin levels are linked to lower blood pressure and heart rate in premenopausal women
In animals, ventral stroking for &gt;5 days increases oxytocin (OT) activity and decreases blood pressure (BP), but related human studies are few. Thus, relationships between self-reported frequency of partner hugs, plasma OT and BP levels were examined in 59 premenopausal women before and after warm contact with their husbands/partners ending with hugs. Higher baseline OT before partner contact was associated with lower BP and heart rate, and met criteria to be a partial mediator of the lower resting BP shown by women reporting more frequent hugs (P &lt; 0.05). OT levels during post-contact stress were unrelated to hugs or BP. Menstrual cycle phase did not influence any OT measure. Thus, frequent hugs between spouses/partners are associated with lower BP and higher OT levels in premenopausal women; OT-mediated reduction in central adrenergic activity and peripheral effects of OT on the heart and vasculature are pathways to examine in future research.

Also, other transmitter systems are involved in what we might characterise as affectionate behaviour. the opioid system has a role in both humans and non-human primates:
In non-human primates:

Opioid receptor blockade reduces maternal affect and social grooming in rhesus monkeys
Seven lactating female rhesus macaques, housed in social groups, were administered with low doses (0.5 mg/kg) of the opioid antagonist naloxone when their infants were 4, 6, 8, and 10 weeks old. A control group received saline. Mothers receiving naloxone were involved in less grooming with other group members, and were less protective towards their infants. By infant-age week 8 they also groomed their infants less, while other monkeys groomed the infants more. Other behavioural measures of mother-infant interactions were not altered. With time, from infant-age week 6 onwards, some short-lived dysphoric conditioned drug responses to naloxone became apparent, although these were not correlated with the decline in social interaction. These results are interpreted in terms of possible interference of naloxone with maternal affect.

And humans:

Social touch modulates endogenous μ-opioid system activity in humans
In non-human primates, opioid-receptor blockade increases social
grooming, and the endogenous opioid system has therefore been
hypothesized to support maintenance of long-term relationships in
humans as well. Here we tested whether social touch modulates
opioidergic activation in humans using in vivo positron emission
tomography (PET). Eighteen male participants underwent two PET scans
with [11C]carfentanil, a ligand specific to μ-opioid receptors (MOR).
During the social touch scan, the participants lay in the scanner
while their partners caressed their bodies in a non-sexual fashion. In
the baseline scan, participants lay alone in the scanner. Social touch
triggered pleasurable sensations and increased MOR availability in the
thalamus, striatum, and frontal, cingulate, and insular cortices.
Modulation of activity of the opioid system by social touching might
provide a neurochemical mechanism reinforcing social bonds between
humans.