if both people are now orthodox and didn't have an orthodox wedding, most places would consider them married, give them Holy Communion but also invite them to have an orthodox wedding.
i think from what people have said above that catholic weddings may be counted.
i know civil weddings are not, and i suppose with protestant weddings, it depends on the circumstances.
last weekend my friends had their church wedding (now they are both orthodox); they had only had a civil wedding before. this was because of complicated circumstances relating to them being from different countries and living in a third country.
it was extremely beautiful and they and their guests from other countries and all the church people were very blessed.
i wouldn't look at it as 'having to have another wedding', but as 'getting a second chance to take part in all the blessings and prayers which were missed the first time around'.
also you get to wear pretty clothes and have a party and invite your sceptical friends to church! (they may not want to come on a regular day, but would make the effort for your special celebration)