Species Identification: Red velvety insect, India
As you might have noticed from its appearance, this is a red velvet mite. This is an arachnid (related to spiders) and not an insect.

The red velvet mite apparently does not bite or sting (according to this website), and it is also used for medicinal purposes in India, according to this Wikipedia image, so it is unlikely to be dangerous. 



If you haven't seen it already, the webcomic The Oatmeal has an amusing take on some of the arthropod's mating habits.