Does Islam Encourage Large Families?
Question

I noticed that people are of two types: those who encourage us to have few children and those who encourage us to have a lot of children. Is there evidence to support either of these two opinions?
Praise be to Allah.Blessings of having children
Abu Dawud (2050) narrated that Ma’qil ibn Yasar said: A man came to the Prophet (peace and blessings of Allah be upon him) and said, “I have found a woman who is of good lineage and is beautiful, but she does not bear children. Should I marry her?” He said, “No.” Then he came again with the same question and he told him not to marry her. Then he came a third time with the same question and he said: “Marry those who are loving and fertile, for I will be proud of your great numbers before the other nations.” (Classed as sahih by al-Albani in Irwa al-Ghalil, 1784). 
This hadith indicates that it is encouraged to marry women who are fertile, so that the numbers of the ummah will increase, and so the Prophet (peace and blessings of Allah be upon him) will feel proud of his ummah before all other nations. This shows that it is encouraged to have a lot of children. 
Will you be rewarded for having children?
Al-Ghazali said that when a man gets married, intending thereby to have children , that this is an act of worship for which he will be rewarded because of his good intention. He explained that in several ways: 

This is in accordance with what Allah wants, which is to perpetuate the human race. 
Seeking the love of the Messenger (peace and blessings of Allah be upon him) in having many children, so that he will feel proud of them before the other Prophets and nations on the Day of Resurrection. 
Seeking barakah (blessing) and a great deal of reward, and forgiveness of sins through the du`a of a righteous child after one dies. 

Having children was the hope of the Prophets and Messengers
It is well known that since ancient times children have been the hope of the Prophets and Messengers and all of the righteous slaves of Allah, and that will continue to be the case so long as man’s innate nature (fitrah) remains sound. Children are a blessing whom people love and on whom they pin their hopes. 
Ibrahim (peace be upon him) prayed to his Lord, saying (interpretation of the meaning): 
“My Lord! Grant me (offspring) from the righteous” [al-Saffat 37:100]
And Allah says of Zakariyya (peace be upon him) (interpretation of the meaning): 
“When he called out to his Lord (Allah) a call in secret.
He said: ‘My Lord! Indeed my bones have grown feeble, and grey hair has spread on my head, and I have never been unblest in my invocation to You, O my Lord!
And verily, I fear my relatives after me, and my wife is barren. So give me from Yourself an heir.
Who shall inherit me, and inherit (also) the posterity of Ya’qub (Jacob) (inheritance of the religious knowledge and Prophethood, not of wealth). And make him, my Lord, one with whom You are Well-Pleased!’
(Allah said) ‘O Zakariyya (Zachariah)! Verily, We give you the glad tidings of a son, whose name will be Yahya (John). We have given that name to none before (him)’” [Maryam 19:3-7]
Allah praises His righteous slaves in many ways, such as when He said (interpretation of the meaning): 
“And those who say: ‘Our Lord! Bestow on us from our wives and our offspring the comfort of our eyes, and make us leaders of the Muttaqun (the pious)’” [al-Furqan 25:74]
And Allah tells us that Shu’ayb (peace be upon him) commanded his people to remember Allah’s blessing to them when He made them many after they had been few. He said (interpretation of the meaning): 
“And remember when you were but few, and He multiplied you” [al-A’raf 7:86]
He regarded their being multiplied after they had been few as a great blessing which obliged them to obey Allah and obey His Messenger (peace and blessings of Allah be upon him). 
Undoubtedly the benefits of increasing the nation’s offspring are obvious to everyone who thinks about the matter. Hence nations who understand this matter have been keen to encourage their people to increase their numbers and also to make their enemies reduce their numbers by means of specious arguments and sometimes by using means that lead to infertility and having few children, by means of drugs, contaminated food stuffs that reduce fertility and so on. This is one of the means of war used against the Muslim ummah by its enemies. 
We ask Allah to ward off the evil of those who disbelieve and to thwart their plots against the Muslims. 
For more, please see this category: Fiqh of the Family
And Allah knows best.