“neither marry nor are given in marriage.” This phrase exactly represents the biblical culture. Men marry, while women are “given in marriage.”
“but are as the angels in heaven.” The assumption is that angels do not marry and have families. That will be the case with us in the next life. There are some important things to pay attention to in this verse. One is that Jesus said we will be like the angels, not that we become angels. There are people who believe when a believer dies, he or she goes to heaven and becomes an angel. That is not the case. Dead believers do not become angels. The context of this section is marriage, and when it comes to marriage, resurrected believers will be like angels in that they do not marry.
Also, this verse comes as close as any to addressing the question about whether or not there will be sexual intercourse in the next life, but it does not settle the issue completely. It is possible but unlikely that angels have sexual intercourse. There is no indication in Scripture that angels participate in sexual intercourse with each other, even though there are both male and female spirit beings in the Bible (cp. Zech. 5:9). The most likely case is that human sexual drive was given by God to insure the future of the race, and that there will be no sexual drive in our new bodies. Without any sexual drive or desire, there would be little point to sexual intercourse. It is true that sexual intercourse is exciting and fulfilling here on earth, but again, that is most likely God’s design for life here and now so that the human race would continue.
Many people ask about the nature of personal relationships in the next life: for example, will people in a wonderful marriage still be friends even if they are not married? In the next life we will know the people we knew in this life. Just as Jesus came back from the dead in his new body and knew everyone he had known on earth, we are promised that in our new bodies, “I will know fully even as also I was fully known” (1 Cor. 13:12).
However, the kind of relationships people who were married on earth will have in the future is not answered in the Bible beyond it simply saying that people who are married on earth will not be married in the next life. One likely reason for that is that relationships are complex. For example, the woman the Sadducees were using as an example had been married to seven different men (Matt. 22:25-28). It is probable that she liked or even loved some of them, and just as probable that she did not like others but married them out of duty to the Mosaic Law (Deut. 25:5-10).
Marriages on earth are very complex: some are wonderful relationships; some are a continual battle, often including adultery and even occasionally murdering the spouse; some people marry multiple times; and there are many other permutations of the marriage relationship. Some people would love for their marriage to continue as a friendship in the next life while other people would not even want to be friends with the person they had been married to. Given all that, we can see why God does not give us a better glimpse of the next life—it would just lead to more questions. On the other hand, the Bible does promise happiness and joy in the next life, so there is some reason to believe that people who have had horrible relationships will be delivered from those, while people who have been in wonderful relationships might well have those relationships continue. Thankfully, because God is a Father and a God who loves family, and because He does promise joy in the next life, no matter what our relationships are on earth, we can look for joyful ones in the next life.