I. Cultural/ Religious Similarity:
I was recently watching Oshin, the famous jdorama and saw a scene with a Japanese "doll" festival (hinamatsuri). Here is a snap of the doll arrangement (on 7-tiers) during the Hinamatsuri festival. 
To people from
South India, this will be strikingly reminescent of the "Golu"
arrangement during the Navarathri (nine nights) festival. Among Hindu festival
practices, the practice of Golu is a remarkable anomaly: while Navarathri is
celebrated all over , the Golu doll arrangement is almost exclusivel to India South India! Here is a snap of a typical Golu with the same 7 (always an odd number
of) tiers! .
Interestingly, both festivals are in honor of women/girls, although this may be explained by the gender stereotype of the association of girls and dolls.
II. Linguistic/cultural similarity: Common linguistic expression for not-so-common occurrences
Whenever a rare event occurred, such as my waking up before 8 am on a weekend, my mom would exclaim (in Tamil): "It is going to rain heavily"! I have heard an identical expression used in Japanese anime when rare events occur: the Japanese actually say either 雪がふる (it is going to snow) or 雨がふる (it is going to rain).
I have also verified with native Japanese speaker friends that this is indeed a common expression for not-so-common occurrences. Does any other language have a similar/identical expression? I would love to hear if yours does, so feel free to leave a comment.
Of course one cannot rule out the possibility of convergent evolution here, with an unpredictable weather related phenomenon being the common denominator. But whereas rain is fairly rare in south India, at least in the city of
from which yours truly hails, it is almost certainly not
as rare in Chennai from what I hear of summer weather there.
However, this similarity is a classic example of how hard it would be for
anyone not having had conversations with Tamil speakers to even guess at the
common usage of these expressions. Japan
III. Cultural Similarity: Uchimizu (Vaasal thelippadhu)
Uchimizu is defined as " old custom of sprinkling water with a ladle on streets and gardens", and according to wikipedia "has [in addition to hygeiene] a ritual or contemplative purpose" (some children practising uchimizu pictured below) [20, 21].
An identical practice, called, vaasal thelippadu , is an ancient tradition commonly practiced by the women of the house in S.India (and not commonly in N.India) as far as I know. In the early mornings (and sometimes evenings), women sprinkle water on the earth, and lay down a complex pattern of closed curves, often with rice flour, called a kolam, believed to be a "talisman" for bringing prosperity and warding off evil. Even though this is practiced every single day, in almost every single household I know of (even crossing religious boundaries), I could not find a single picture of this practice on the internet, indicating how difficult it can be for someone to appreciate/understand local customs without actually traveling to South India, and seeing them first-hand.
IV. Art-form similarity: Tsuzumi/Udukkai
A common instrument used in Japanese theater is the tsuzumi, which often appears in pairs (picture below). According to wikipedia: "A single drum head is struck with the tips of the fingers of one hand to produce a distinct "pon" sound, while the other hand holds the drum by its cords, squeezing or releasing them to change the pitch of the drum. Depending on how the player tightens or releases the cords of the tsuzumi, and how hard or soft one strikes the head with one's hands, the tsuzumi can produce a range of sounds."
An identical drum used in folk music of S.India is the udukkai pictured below. Having played the udukkai myself once for a concert, I can attest to the fact that the manner of playing is identical to that described above for the tsuzumi.
Since the udukkai is a very old S.indian instrument (it is commonly pictured as being held by the Saivite diety Nataraja of a very ancient S.Indian religious tradition), exploring this relationship could lead to interesting facts/dates about of the transmission of art-forms, and the tsuzumi in particular.
V. Similarities in religion
Here is a Shinto temple from Japan, 
Here is a Shinto temple from Japan, 
and a Hindu temple from Guruvayoor, Kerala (Malayalam speaking region) with its architectural style peculiar only to Kerala (in S.India) .
The sloping style of roofs and the like could be a classic case of parallel evolution (e.g. characteristic of regions with heavy rainfall), or transmitted across east Asia (the architecture style is reminescent of Buddhist temples across east Asia). More research is needed to verify if the architectural similarities are more than superficial.
Now let us zoom in to the two posts on either side of the entrance to the Shinto temple. Here is a photograph of them side by side.
While I actually don't know what purpose these posts serve, are they reminescent of the kuttru vilakku (traditional South Indian oil-lamp, below)?
Here is a shrine of a typical (rural) south Indian diety (Aiyanaar). Notice the red-white markings on the doorstep and the lamp in front of the shrine.
I have seen similar red-white markings on Japanese shinto shrines. The red-white markings are apparently a common theme in Chinese worship, although I am yet to find pictorial evidence for either. Any experts on Japanses/Chinese religion?
I am currently researching a variety of similarities in other socio-cultural spheres including: (i) layout of religious shrines, (ii) art forms (kabuki vs. kathakali), (iii) social practices, and even (iv) cuisines! These sections will be appear in the coming months.