I shall mention a few that I have personally been to and I have been told/witnessed these myself.
Chidambaram Thillai Nataraja Temple, Chidambaram, Tamil Nadu
The temple is run by the Pothu Deekshitars who are believed to have been brought down from Mount Kailas by Lord Nataraja Himself. They are the traditional owners and trustees of the temple. The temple and its premises were forcibly taken over by greedy politicians and bureaucrats to feed off their revenue. In a landmark judgment in 2014, the Supreme Court asked the state to return the temple back to the rightful owners (SC frees Nataraja temple from TN Govt's control)
Only married men are allowed to touch the idol and do the daily poojas.
Only men who have hair on their heads and are able to grow it into a length long enough to tie it into a kudumi (bun) are allowed to be priests. (Tamil Nadu's Dikshitars on the verge of extinction)
Thirunelli Maha Vishnu Temple, Wayanad, Kerala
Before there were motors, people had to carry and bring up pots of water up to the top of the hill where this temple is situated for conducting the daily rituals. Once a local elite lady saw the suffering of the people and commissioned a granite/stone waterway to be built from a stream downhill from where the people used to collect water all the way up to the temple. The waterway still stands even to this day. Not an ounce of mortar or any binding agent has been used to bind the stones together. the rocks just fit together and water flows UPHILL. Even now, it is is this water that is used for daily poojas in the temple. I have actually gone and stood under the waterway to see if any leakage is there. Nope. Nothing.
Kashi Vishwanath Temple, Varanasi, Uttar Pradesh
In the entire city of Kashi, it is said that no flowers will emit any fragrance. Dogs will not bark. And lizards will not chitter. Kashi is said to be a cremation ground.
Anegudde Sri Vinayaka Temple, Kumbhashi, Udupi, Karnataka
The idol in this temple grows in size. Lord Vinayaka of Anegudde wears a silver armor/ breastplate which has to be changed frequently because it would break at the sides after a while due to the idol growing in size.
Sree Poornathrayeesa Temple, Tripunithura, Kerala
This is probably the only temple where the idol of Lord Ganesha faces the South direction. As per temple legends, the idol of Lord Poornathryeesha was brought down from Vaikuntham by the Pandava prince Arjuna and Lord Krishna to commemorate their visit to bring back the Brahmin’s children (a story in the Mahabharata). It was Arjuna who was carrying the idol and he requested Lord Ganesha to go ahead of him and find a good place to consecrate the idol. Lord Ganesha found a spot in Poornavedapuri on the banks of the Poorna river to be the most auspicious spot. Poornavedapuri got its name as it was one of the main centers of Vedic teaching in the region. Lord Ganesha found the spot to be so auspicious that He occupied the spot Himself. When Arjuna arrived at the scene carrying the idol in his hands, he saw Lord Ganesha seated comfortably at the ordained spot. Arjuna requested Lord Ganesha to move, but He would not budge. Arjuna could not keep the idol down anywhere else as it would be fixed to that spot thereafter. After repeated requests, Lord Ganesha refused to move an inch. The idol was growing heavier in his arms and Arjuna could bear it no longer. It is said that he gave a shove to Lord Ganesha with his foot to the left side and placed the idol of Lord Vishnu at the same spot.
Chottanikkara Bhagavathi Temple, Chottanikkara, Kerala
This temple is the ultimate testimony of the importance of Shaktya tradition of worship and of the importance of Tantric practices being followed in Kerala. The deity here is that of the female goddess who is worshipped as Goddess Saraswati in the morning, as Goddess Lakshmi at noon and as Goddess Parvati/Shakti in the evening.
Mannarasala Sree Nagaraja Temple, Alappuzha, Kerala
The priest here is the oldest female member of the Namboothiri family which is the traditional owners of the temple as she is said to symbolize the mother of Lord Nagaraja, the main deity there. Only she is allowed to do the main pujas in the temple.
After her death, the next oldest female member assumes the position.
Sree Pattabhirama Temple, Tripunithura, Kerala
The temple is owned and run by the Goud Saraswat Brahmin community. It is prohibited for anybody from any other caste to enter the main shrine of Lord Pattabhirama. A lot of people, however, visit the temple and stand outside the main shrine to pray. The small shrine of Lord Hanuman located to the left of the main entrance also draws a lot of devotees every day.