A wedding ring is symbolic of many spiritual concepts and truths, and there are many laws and customs pertaining to it. It is interesting to note that although it is universally accepted Jewish custom to use a ring to affect the marriage, from a purely technical standpoint, the ring itself is merely a custom; the Talmud contains no actual reference to it.
Technically, the groom needs only to give the bride a gift of value (worth at least a perutah, a small coin used in Talmudic times). He could instead give her a cell phone or a blender and... mazel tov, they're married!
We won't delve into all the mystical symbolism of the wedding ring. However, in order to answer the question, let's examine what the ring given at a Jewish wedding represents legally, in terms of the validity of the wedding.
According to Jewish law, there are different ways to purchase something. One method is by giving cash, kesef. When a groom gives something of value (a ring or blender) to the bride, he is obviously not buying her. She is a human being, not a piece of property. So this is not a perfect analogy. However, he is acquiring exclusive rights to her hand in marriage. From this moment onwards no other man can be intimate with her. Thus the ring isn't merely a sentimental gift given to the beloved; it actually effects the "transaction."
When a woman gives a man a ring in return, they are simply exchanging articles of value. They could exchange blenders, too...When a woman gives a man a ring in return, they are simply exchanging articles of value. They could exchange blenders, too. Now they have just made a trade, and not effected a change of her status, to a married woman. The legal transaction implied by the groom giving the bride a ring has now been matched one for one, and thereby cancelled. Her status remains unchanged. It is as if the bride has not received anything at all, or as if she has given back the gift.
One may ask, but what about the feelings and intentions of the groom and/or bride as they give their rings? Don't the feelings and intentions count for something? What if the bride has in mind that she is giving a ring simply to express her profound love for her groom, and not for any legal purpose?
Nevertheless, a) the external factor is quite compelling. While one couple may have this intention, another may not. b) When dealing with a ceremony as sensitive and important as marriage – a ceremony whose ramifications will (hopefully) affect all future generations, we want to avoid even the appearance of impropriety.
Under the chupah, the groom recites the words "You are betrothed to me...according to the laws of Moses and Israel." It is important, especially in matters with long-lasting ramifications such as a wedding, that we put aside our own desires and ask ourselves, what is the Torah really asking of me, and what is the law?
Jewish marriage is known as "kiddushin," which means holiness and separation. A Jewish bride and groom elevate themselves to new heights of holiness by going through a proper Jewish wedding ceremony. When it comes to such momentous occasions in life, it is important to respect halachah, so as to avoid creating any doubt.
If the bride feels that she must give a ring to your groom, it may possibly be done after the chupah is over, in private.
Getting married in a manner that is fully in keeping with Jewish law is the best way to start out your life together with blessings and happiness!