Not like we do now on earth. The best insight on this comes from Matthew 22:23-33. Jesus, in answering a different question, says that those in the resurrection do not marry, nor are they given in marriage. Apparently, then, marriage is a part of this current life and not of the life to come.
“Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God. For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.” (Matthew 22:29-30)
It is more than likely that Jesus means not just the ceremony of marriage but all the roles, duties and physical intimacies as well. In fact, Jesus further says that we will be like the angels in Heaven; that is, angels are interdimensional beings who are able to move easily between the spiritual and material dimensions. We also know that we will have immortal bodies (1 Cor. 15:53).
This does not mean there will be no relationship between those who were married on earth when they reach Heaven. We will know each other and love each other to an infinite degree at that point. Any relationship, though, in Heaven, will be quite different than those we have here on earth.