There are several different ways to signify the unity of two people. Here is a list of various ways that could be used in any wedding ceremony.
The Unity Candle: This is probably the most common of the unity ceremonies. The bride and groom each take a lit candle and simultaneously light a third larger "unity candle." They may blow out their individual lights, or leave them lit, symbolizing that they have not lost their individuality in their unity. You can make this more unique by picking candles that are not ‘run of the mill’ unity candles.
Water/Sand Ceremony: The couple each pours different colored water or sand into a single glass, creating a third color with the water, or a layered look with the sand. The new mixture cannot be separated into it’s original halves, signifying a life long, irreversible bond.
Wine Ceremony: The bride and groom each take a carafe of wine and pour it into a single glass, which they both drink from. Just like the water and sand ceremony, the parts, once mixed cannot be separated. Additionally, the couple drinks the wine, symbolizing how their love nourishes them.
Rose Ceremony: This is a simple unity ceremony where the bride and groom exchange roses. Other variations include the families exchanging roses, or even the bride and groom making a bouquet together using two different types of flowers- one for each of them.
Garland Ceremony or Lei Ceremony: The bride and groom exchange garlands of flowers. This is a common part of Indian weddings. It represents their new unity, blessed by nature. In Hawaian weddings, the bride and groom typically exchange leis. The families may also exchange leis with the couple. Leis represent the love and respect you have for the person you are giving it to, and the unity of the new family.
Circling: In Eastern European ceremonies, the bride and groom circle the altar three times, which are their first steps together as husband and wife. The unbroken circle represents the unbroken commitment to each other.
Broom Jumping: Typically the family places the broom on the ground, and the bride and groom jump over it together. The broom can then decorate a place of honor in their home.
Planting: A couple with at least one green thumb can plant seeds or a sapling. Its growth would be a reflection of their love and lives together.
Hand Tying: This is just what it sounds like. The officiate literally ties the couples hands together to signify their bond.
Other ideas that have been suggested (probably in jest) are sandwich making and feeding it to eachother, s'more making, and making a simple painting (one the spot with everyone watching! Eek!)
Clearly there is a ceremony for every couple!