According to an article in the New York Times by Peggy Post, director of the Emily Post Institute, guests at a second wedding who gave gifts at either the bride's or the groom's first wedding shouldn't be expected to bring a gift the second time around. However, gifts are mandatory at bridal showers, no matter how many weddings the bride has had.
This rule holds even if it is been years or even decades since the first wedding. Some guests prefer to bring a gift even if gifts are not requested or wanted. As gracious hosts, the bride and groom are obligated to make them feel comfortable doing so.
With a second marriage, it is likely the bride or groom or both has an established household. In order to not have two of everything, or plates and silverware in the wrong pattern, it is appropriate to establish a small registry. It is also fine to ask guests who wish to bring a gift to donate to a charity or toward a honeymoon fund instead of bringing a gift. While the wedding invitation is not the place to include information about gifts or registries, it is fine to put a small section about the gift policy on a wedding website along with a link to a registry. It is also perfectly fine to handle it the old-fashioned way: using word-of-mouth.
When unsure whether or not to bring a gift, guests should opt for a small gift, particularly something personal like a small family heirloom. Even a bottle of wine will suffice.