In many temples, I have seen people praise the tail of a cow instead of its head or legs (which are common). Praising the head of a cow is said to be counted as a sin. What is the reason behind this? Is there any mythological story about this practice?
The Shiva Mahapurana describes an incident when Lord Rama, Sita, and Lakshman heard of the death of King Dashratha. Rama & Lakshmana left to find the required items for the shraddha ceremony. When Rama did not return in time, Sita performed them on his behalf.
When Rama returned and Sita told him what she had done, she called on four witnesses: the Falgu river, a Ketaki bush, the fire, and a cow. All denied telling the truth, including the cow. While the cow's mouth lied, the tail, however, shook in agreement with Sita. After Lord Surya appeared and attested to her truth, Sita cursed the four false witnesses: the Falgu river to disappear underground, the Ketaki to never be offered to Lord Shiva, the fire to eat everything indiscriminately, and the cow's mouth to be impure. The hindquarters of the cow remained pure.
The back of the Cow is considered the most auspicious because, as per scriptures Goddess Lakshmi resides there. This is corroborated by Mahabharata also. That is the reason cow dung, urine is also considered very auspicious, not because of other stories. That is reason in all the temples in south India, when the temple doors are open early in the morning, Cow is made to enter with back facing the deity. This is because it is auspicious as Mother goddess Lakshmi resides there and sanctifies all.
Also, Goddess Lakshmi, the consort of Lord Vishnu is auspiciousness of all that is auspicious (She is the ulimate Shiva (auspiciousness)) That is why, in many temples, people praise the tail/back of a cow.