At Jewish weddings brides typically wear wedding dresses like you'd find at other weddings. The veil is a bit more common because the unveiling of the bride is part of the traditional Jewish bedeken ceremony.
Most grooms dress in suits. Some also wear a tallis, a Jewish prayer shawl with knotted fringes on the end. More traditional grooms wear a kittel, a belted white robe that symbolizes purity.
In some Jewish ceremonies, modeled after Sephardic tradition, the couple may be wrapped in a large tallis during some portion of the wedding ceremony when blessings are recited. It is often used for the final benediction. This ritual is adaptable for any wedding.