Must all Mormons marry and have children? Mormonism believes "that God’s [first] commandment for His children to multiply and replenish the earth [Gen. 1:28] remains in force". Does this mean all Mormons must marry and have children? Or can some be perpetual virgins? What about infertile or childless marriages?
Does this mean all Mormons must marry and have children?

'Must' is a strong word, Mormons believe in agency: the ability and privilege God gives us to choose and to act for ourselves. As with all commandments, Mormons believe we have a choice, however, if we want the blessings, promises, or protection a commandment brings then we should/will make the choice to keep God's commandments.
If a Mormon wants to attain exaltation, the highest glory of the celestial kingdom, then they must marry, be sealed, and live faithfully to their covenant.1
The Family Proclamation restates the command given in Genesis 1:28 for families:

to multiply and replenish the earth

and while there is not a specific blessing attached to this command, we know that God blesses us for keeping the commandments. So if you want the potential blessings yes.2

Or can some be perpetual virgins?

Yes, because Mormons believe in agency, no if they want the same blessings and promises to those who are sealed.

What about infertile or childless marriages?

God knows the intents and desires of our hearts.3 Mosiah 4:24-25 says:

24 And again, I say unto the poor, ye who have not and yet have sufficient, that ye remain from day to day; I mean all you who deny the beggar, because ye have not; I would that ye say in your hearts that: I give not because I have not, but if I had I would give.
25 And now, if ye say this in your hearts ye remain guiltless, otherwise ye are condemned; and your condemnation is just for ye covet that which ye have not received.

This lets us know that God will judge us based on our desires. So if we have righteous desires but are unable to act on them for some reason we can still attain the blessings.

President Harold B. Lee relied on these scriptures in another example:
“[Women] who have been denied the blessings of wifehood or motherhood in this life—who say in their heart, if I could have done, I would have done, or I would give if I had, but I cannot for I have not—the Lord will bless you as though you had done, and the world to come will compensate for those who desire in their hearts the righteous blessings that they were not able to have because of no fault of their own.” (Ye Are the Light of the World, Salt Lake City: Deseret Book Co., 1974, p. 292.)4


Because in the context of the LDS Church, where the family is celebrated as the fundamental unit of society, childlessness can be an especially difficult challenge. There are many articles to address those facing infertility:

Faith and Infertility By Melissa Merrill
Faith and Infertility An Ensign Online Exclusive
Many more

1 https://www.lds.org/scriptures/dc-testament/dc/131.1-4
2 D&amp;C 130:20-21, D&amp;C 14:7
3 Hebrews 4:12-13 and https://www.lds.org/scriptures/tg/god-omniscience-of?lang=eng
4 The Desires of our Heart