Benefits of Being a Hafiz
Question

What are the benefits that a Hafiz gets in this life and the next? And what about his relatives and offspring? What about the generations before and after him?
Praise be to Allah.Benefits of memorizing the Quran 
Memorizing the Quran is an act of worship through which one seeks the Face of Allah and reward in the Hereafter. Without this intention, he will never have any reward , rather he will be punished for doing this act of worship for someone or something other than Allah. 
The hafiz (the person who has memorized the Quran) should not have any intention of gaining worldly benefits by memorizing the Quran , because his memorization thereof is not a product to be traded with in this world, rather it is an act of worship which is done for the sake of his Lord.
Benefits of being a Hafiz in this world 
Allah has given special privileges to the one who memorizes the Quran in a number of ways in this world and in the Hereafter, for example:

He takes precedence over others in leading the prayer.

 It was narrated that Abu Mas’ud al-Ansari said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘The people should be led in prayer by the one among them who has the most knowledge of the Book of Allah; if they are equal in knowledge of the Quran, then by the one who has most knowledge of the Sunnah; if they are equal in knowledge of the Sunnah, then by the one who migrated (made hijrah) first; if they are equal in terms of hijrah, then by the one who became Muslim first. No man should lead another in prayer in his domain of authority, or sit in his place in his house, except with his permission.” (Narrated by Muslim, 673) 
`Abd-Allah ibn `Umar said: “When the first Muhaajirun (emigrants) came to Quba, before the Messenger of Allah (peace and blessings of Allah be upon him) came (to Madinah), Salim the freed slave of Abu Hudhayfah used to lead them in prayer, and he was the one who knew the most Quran.” (Narrated by al-Bukhari, 660)

He is placed in front of others in a common grave, closer to the qiblah, if it is essential to bury him with others.

Jabir ibn ‘Abd-Allah (may Allah be pleased with them both) said: “The Prophet would wrap two of the men slain at Uhud in a single cloth, then he would ask, ‘Which of them knew more Quran?’ If one of them was pointed out to him, he would put that one in the lahd (niche in the side of the grave) first. And he said, ‘I will be a witness over these people on the Day of Resurrection.’ He commanded that they should be buried with their blood, without being washed, and that no funeral prayer should be offered for them.” (Narrated by al-Bukhari, 1278)

He takes precedence in leadership if he is able to bear that.

‘Amir ibn Wathilah narrated that Nafi’ ibn ‘Abd al-Harith met ‘Umar in ‘Usfan, and ‘Umar had appointed him as governor of Makkah. ‘Umar said, “Who have you appointed in charge of the people of the valley?” He said, “Ibn Abza.” ‘Umar asked, “Who is Ibn Abza?” He said, “One of our freed slaves.” Umar said, “Have you appointed over them a freed slave?!” He said, “He is well-versed in the Book of Allah and he has knowledge of the laws of inheritance.” ‘Umar said: “Your Prophet (peace and blessings of Allah be upon him) said: ‘Indeed, by this Book, Allah would exalt some people and degrade others.’” (Narrated by Muslim, 817)
 Benefits of being a Hafiz in the Hereafter

The status of the one who memorizes the Quran will be commensurate with the last verse he memorized. 

‘Abd-Allah ibn ‘Amr narrated that the Prophet (peace and blessings of Allah be upon him) said: “It will be said to the companion of the Quran (i.e., the one who memorized and studied it): ‘Read, advance in status and recite as you used to do in the world, for your status will be commensurate with the last verse that you recite.’” (Narrated by al-Tirmidhi, 2914; he said this is a sahih hasan hadith. Al-Albani said in Sahih al-Tirmidhi, no. 2329, it is hasan sahih. Also narrated by Abu Dawud, 1464)
 What is meant by reciting here is memorizing.

He will be with the angels, accompanying them. 

`Aishah that the Prophet (peace and blessings of Allah be upon him) said: “The one who recites the Quran and learns it by heart, will be with the noble righteous scribes (in Heaven) and the one who exerts himself to learn the Quran by heart and recites it with great difficulty, will have a double reward.”  (Narrated by al-Bukhari, 4653; Muslim, 798) 

He will be given a crown of honour and a garment of honour to wear. 

Abu Hurayrah narrated that the Prophet (peace and blessings of Allah be upon him) said: “The Quran will come on the Day of Resurrection and will say, ‘O Lord, adorn him.’ So he will be given a crown of honour to wear. Then it will say, ‘O Lord, give him more.’ So he will be given a garment of honour.’ Then it will say, ‘O Lord, be pleased with him.’ So Allah will be pleased with him. Then it will be said to him, ‘Recite and advance in status, and for each verse you will gain one more hasanah (reward for good deed).” (Narrated by al-Tirmidhi, 2915. He said, this is a sahih hasan hadith. Al-Albani said in Sahih al-Tirmidhi, 2328, this is hasan)

The Quran will intercede for him with his Lord. 

Abu Umamah al-Bahili said: “I heard the Messenger of Allah (peace and blessings of Allah be upon him) say, ‘Recite the Quran, for it will come on the Day of Resurrection to intercede for its companions . Recite the two bright ones, al-Baqarah and Surah Al ‘Imran, for they will come on the Day of Resurrection like two clouds or two shades or two flocks of birds in ranks, pleading for those who recite them. Recite Surah al-Baqarah for to take recourse to it is a blessing and to give it up is a cause of grief, and the magicians cannot confront it.”  (Narrated by Muslim, 804, and by al-Bukhari in a mu’allaq report)
Rewards for relatives and descendants of the hafiz
With regard to his relatives and descendants, there is evidence concerning his parents that they will be clothed with garments which far surpass everything to be found in this world, and that will only be because they took care of and taught their child. Even if they themselves were ignorant, Allah will honour them because of their child. But the one who prevented his child from learning the Quran, he will be one of those who are deprived. 
Abu Hurayrah said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘The Quran will come on the Day of Resurrection like a pale man saying to its companion, “Do you recognize me? I am the one who made you stay up at night and made you thirsty during the day…” Then he will be given dominion in his right hand and eternity in his left, and a crown of dignity will be placed upon his head, and his parents will be clothed with garments which far surpass everything to be found in this world. They will say, “O Lord, how did we earn this.” It will be said to them, “Because you taught your child the Quran.”’” (Narrated by al-Tabarani in al-Awsat, 6/51)
Buraydah said: “The Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Whoever reads the Quran, learns it and acts in accordance with it, on the Day of Resurrection his parents will be given a crown to wear whose light will be like the light of the sun, and his parents will be given garments which far surpass everything to be found in this world. They will say, “Why have we been given this to wear?” It will be said, “Because your child learned the Quran.”’” (Narrated by al-Hakim, 1/756)
 These two hadiths support one another. See al-Silsilah al-Sahihah, 2829. 
And Allah knows best.