Breaking a glass
The most famous custom in memory of the destruction of the Temple is the bridegroom smashing a glass at the end of the wedding ceremony. Some Eastern communities broke a piece of pottery. There was a custom in Russia of throwing the glass against a wall instead. Today there are websites offering to suspend the shards of your glass in a tasteful leucite sculpture.
Other reasons are given for the custom, whose source is in Talmud Berachot, 31a, where we read that Mar, the son of Ravina, smashed a glass goblet worth 400 zuz at his son's wedding party because he thought that the rejoicing was getting out of hand.
The Talmud explains that in our broken world it is not right to surrender utterly to full-blown laughter and rejoicing: one should somewhere remind oneself that there is suffering and brokenness in the world even in the midst of our celebration. This encompasses, but also goes beyond, our sadness about the Temple.
Another beautiful reason for the custom, cited by Aryeh Kaplan, is that just as a glass can be glued together and repaired, so too, no matter how broken the bride and groom are when they meet each other, they can help restore each other to wholeness.