Wedding Rings date back to the time of the Egyptians, perhaps even further back. Originally, they were made of woven plant fiber such as papyrus or certain grasses. These were later replaced by sturdier materials, leather, bone, and eventually iron by the time of the Romans. Though gold rings did exist, they were less commonly used up to this point in history for betrothal and weddings.
In the Celtic world, wedding rings were made more popular through the influence of the Romans. The historical record does not seem to show wedding rings or indeed rings being very popular for Celtic people until after the influence of Rome. Often in Rome, the ring also symbolized the joining of a man and a women and often the woman was considered as part of the man's property legally except in some cases involving nobles.
In Celtic culture the perspective was very different. Marriage was treated more like a contract between equals. Each contributed an equal amount of wealth to the marriage. If one survived the other, they would inherit all. Wedding rings came into more common use after the onset of Christianity and this greatly influenced Celtic culture as the Celts endured the Dark Ages and the Middle Ages and so on. By this time, rings had become the staple, even mandatory and it was not uncommon for a poor person to 'rent' a wedding ring for a ceremony and then have to return it to the merchant afterward. By this time gold had become the staple for most wedding rings.
In many parts of the Celtic world the custom of Handfasting was also predominant during this time. A couple would have a trial period, usually of "One Year and a Day" where they would co-habitate and live as man and wife in the same household. If this was successful, there would be a follow up ceremony to 'cement' the marriage. Often during this time a betrothal ring would be worn by the woman which would be replaced by a wedding ring later. The man was not required to wear a betrothal ring.
In Ireland, the now popular 'Claddagh' ring gained popularity as a wedding ring, in the 17th century. Though a recent design, (only 300+ years or so old), it originally was a ring to show fealty to one's lord, who were often English and usually absent from the day to day running of their various estates.
Later it became a betrothal ring complete with it's own set of meaning for how it was worn. Originally inspired from the Galway area of Ireland, it enjoys wide appeal in the UK as well as America and Canada.