Why do Hindus wear necklaces instead of wedding rings?

Thank you to Padma Kuppa for the answer.

First, Hindus may wear wedding rings, but some wear necklaces.

In a Hindu wedding, there is a ritual when the groom ties two pendants – typically gold – with three knots to create the sacred necklace, the mangalasutra – (mangala, auspicious + sutra, symbol). The necklace is a symbol of the commitment the groom offers as he asks the bride to share a long and happy married life. During this mangalya dharanam (wearing of the sacred symbol), the priest chants the following Vedic mantra:

Maangalyam tantunaanena mama jeevana hetunaa: kanThe badhnaami subhage twam jeeva saradaam satam

Which means (roughly):

This is a sacred thread. This is essential for my long life. I tie this around your neck, O maiden having many auspicious attributes! May you live happily for a hundred years (with me).

You can hear it on this video clip from the Tamil movie Alaipayuthey (in Hindi Saathiya):

https://www.youtube.com/watch?v=CcF_IFYp0KQ

The mangalasutra is one of as many as sixteen symbols that indicate marriage for Hindus. The symbols can include a ceremonial bath, a number of symbolic jewelry pieces including the mangalsutra, and skin decoration called Mehendi. Click here for a detailed explanation of the Solah Shringar  and insight into each of the 16 elements that adorn a Hindu bride.

The symbols used in individual weddings vary for Hindus, primarily based on where in India they are from. Socio-economic status also indicates to what extent or how elaborate a particular symbol is. And interestingly, some of the symbols are similar across the different religions from India. I attended a Malayalee Christian wedding many years ago, where the bride was given a necklace that appeared to be similar to mangalasutra (explained below) or another type of necklace with black beads, typically given to brides in some Hindu communities.

In my specific case, as a Telugu (the Indian linguistic community I come from), I had most of the sixteen symbols that a traditional bride is adorned with, and continue to wear some of them on a daily basis – like my mangalsutra, which takes the form of a necklace, as the question poses.

The website Black Book for the Indian Bride presents a myriad of information helpful to an Indian bride, including the rituals and traditions associated with Hindu, Muslim and Christian weddings a la Indian style.