In The Name of Allaah, The Most Merciful, The Bestower of Mercy.
Indeed, Dhikr [remembrance of Allaah] protects a person from shaytaan. Whoever leaves Dhikr, shaytaan will accompany him in that manner in which a person is accompanied by his shadow. Allaah said: [ وَمَن يَعۡشُ عَن ذِكۡرِ ٱلرَّحۡمَـٰنِ نُقَيِّضۡ لَهُ ۥ شَيۡطَـٰنً۬ا فَهُوَ لَهُ ۥ قَرِينٌ-And whosoever turns away (blinds himself) from the remembrance of the Most Beneficent (Allah) (i.e. this Qur’an and worship of Allah), We appoint for him Shaitan (Satan – devil) to be a Qarin (an intimate companion) to him]. [Surah Az-Zukhruf. Aayah 36]
A person is not able to protect himself from shaytaan except through remembrance of Allaah and this one of the magnificent benefits of Dhikr. Imaam Ibnul Qayyim [rahimahullaah] mentioned – in his book titled Al-Waabilus Sayyib – over seventy benefits of Dhikr, and from them are:  Dhikr brings joy, happiness and relaxation in the heart of a person. It makes the heart calm and tranquil, just as Allaah [The Most High] said:
ٱلَّذِينَ ءَامَنُواْ وَتَطۡمَٮِٕنُّ قُلُوبُهُم بِذِكۡرِ ٱللَّهِۗ أَلَا بِذِڪۡرِ ٱللَّهِ تَطۡمَٮِٕنُّ ٱلۡقُلُوبُ
Those who believe (in the Oneness of Allah – Islamic Monotheism), and whose hearts find rest in the remembrance of Allah, Verily, in the remembrance of Allah do hearts find rest. [Surah Ar-Ra’d. Aayah 28].
And the meaning of Allaah’s statement [وَتَطۡمَٮِٕنُّ قُلُوبُهُم – and whose hearts find rest] is that the distress and unease in their hearts will cease and are replaced with cheerfulness, joy and relaxation. And the meaning of Allaah’s statement [أَلَا بِذِڪۡرِ ٱللَّهِ تَطۡمَٮِٕنُّ ٱلۡقُلُوبُ – Verily, in the remembrance of Allah do hearts find rest] is that it has to be the case that nothing else can bring [sound and everlasting] tranquillity [to the heart] except remembrance of Allaah; rather remembrance of Allaah [is the only thing that will give the heart a life based on Eemaan, truth, sincerity, sound guidance, love of good and good deeds, hatred of evil and keeping away from it etc], and [it is the only thing that will nurture] the soul [i.e. in order for it to attain all virtue]. If a person is deprived of remembrance of Alaah, his state is similar to a body that is deprived of its [essential] nourishment. There’s no life [based upon virtue] for the heart except through remembrance of Allaah. And because of this Shaikhul Islaam Ibn Taymiyyah [rahimahullaah] said, ‘’The heart’s [need of] Dhikr is like a fish’s [need] for water, so what will be the state of a fish when isolated from the water!”
When a person remembers Allaah, Allaah remembers him. Allaah said:[فَٱذۡكُرُونِىٓ أَذۡكُرۡكُمۡ– Therefore remember Me [through acts of obedience], I will remember you [by forgiving you].[Ref1] [Surah Al-Baqarah. Aayah 152]
Narrated Aba Hurairah [radiyallaahu-anhu]: The Prophet [sallal laahu-alayhi-wasallam] said that Allaah says, ‘’Whoever remembers Me in himself, I too, remember him in Myself; and if he remembers Me in a group of people, I remember him in a group that is better than them.’’ [Al-Bukhaari 7405]
 From the benefits of Dhikr is that it prevents one from committing sins, wipes away sins and saves a person from Allaah’s punishment. Mu’aadh Ibn Jabal [radiyallaahu-anhu] said that Allaah’s Messenger [sallal laahu alayhi wasallam] said, ‘’The son of Aadam never performs an act that [brings grants] him safety from Allaah’s punishment more than the remembrance of Allaah [The Exalted].’’ [Saheeh Al-Jaami. Number 5633]
 From the benefits of Dhikr is that it earns a person Allaah’s favour, reward and grace [in a way] that a person cannot earn through other acts of worship, even though it [i.e. Dhikr] is the easiest act of worship. That is because moving the tongue is easier than moving the other limbs, for if the movement of the other limbs – day and night – was to be carried out in the same way as the movement of the tongue, a person will face great difficulty; rather he will not be able to do so, but still the reward of Dhikr [with the tongue] carries great good recompense and abundant reward. Abu Hurairah [radiyallaahu anhu] said that the Messenger [sallal laahu alayhi wasallam] said, ‘’If one says one hundred times in a day: ‘None has the right to be worshipped except Allaah, the (Alone), He is the One and has no partner; to Him belongs the kingdom [of the universe] and for Him are all the praises, and He has the power to do everything (the Omnipotent)”, one will get the reward of manumitting ten slaves, and one hundred good deeds will be written in his account, and one hundred bad deeds will be wiped off or erased from his account, and on that day he will be protected from the morning till evening from Satan, and nobody will be superior to him except one who has done more than that which he did.’’ [Al-Bukhaari Numbers 3293 & 6403; Muslim 2691]
The Prophet [sallal laahu alayhi wasallam] said, ‘’Whoever says, ‘Subhaanallaahi Wabi-hamdihee one hundred times a day, will be forgiven all his [minor] sins even if they were as much as the foam of the sea.’’ [Al-Bukhaari. Number 6405]
Abu Hurairah[radiyallaahu anhu] said that Allaah’s Messenger [sallal laahu alayhi wasallam] said, ‘’To say Subhaanallaah, wal-hamadulil laah, Laa Ilaaha Ilal laah and Wallaahu Akbar is more beloved to me than everything over which the sun rises.” [Saheeh Muslim 2695]
 From the benefits of Dhikr is that the plants in Jannah grow by way of it. Paradise- as it has been reported in a hadeeth – is a vast plain with fertile soil and sweet water, and remembrance of Allaah is what makes its plants grow. Ibn Mas’ood [radiyallaahu-anhu] said that Allaah’s Messenger [sallal laahu alayhi wasallam] said, ‘’On the night I was taken up to the heavens, I met Ibraaheem Al-Khaleel [alayhis salaam], so he said to me, ‘O Muhammad! Convey my salaams to your Ummah and tell them that Jannah has fertile soil and sweet water, and it is a Qee’aan [i.e. a plain levelled land], and its cultivation [i.e. what makes its plants grow] is the [utterance] of Subhaanallaah, Alhamdulillaah, Laa ilaaha illallaah and Allaahu Akbar.’’’ [As-Saheehah 105]
Abu Ayyoub Al-Ansaariy [radiyallaahu-anhu] said that when Allaah’s Messenger [sallal laahu alayhi wasallam] met Ibraaheem [alayhis salaam] on the night in which he was taken up to the heavens, [Ibraaheem (alayhis salaam)] said, ‘O Jibreel! Who is with you?’ He [Jibreel (alayhis salaam)] said, ‘This is Muhammad.’’ So, he [Ibraaheem (alayhis salaam)] said, ‘Convey to your Ummah that they increase in what cultivates [the plants of] Jannah, for indeed its soil is fertile and its land is vast.’ So he [Allaah’s Messenger (sallal-laahu-alayhi-wasallam)] said, ‘What is its [means] of cultivation?’ He [Ibraaheem (alayhis salaam)] said, ‘The statement: Laa Hawla Walaa Quwwata Illaa Billaah.’’’ [Musnad Imaam ahmad 5/418. This hadeeth is a witness for the hadeeth before it]
Jaabir [radiyallaahu-anhu] said that the Prophet [sallal-laahu-alayhi-wasallam] said, ‘’Whoever says Subhaanallaahi Wabihamdihee, a palm tree will be planted for him in paradise.’’ [Saheeh Al-Jaami. Number 6429]
 From the benefits of Dhikr is that it is a light for the person in this Dunyah, in his grave and in the hereafter. It [i.e. this light] will be running forward in front of him when he crosses the bridge of Siraat. There is nothing that illuminates the heart and the grave in a manner similar to Dhikr. Allaah [The Exalted] said: [أَوَمَن كَانَ مَيۡتً۬ا فَأَحۡيَيۡنَـٰهُ وَجَعَلۡنَا لَهُ ۥ نُورً۬ا يَمۡشِى بِهِۦ فِى ٱلنَّاسِ كَمَن مَّثَلُهُ ۥ فِى ٱلظُّلُمَـٰتِ لَيۡسَ بِخَارِجٍ۬ مِّنۡہَاۚ – Is he who was dead (without Faith by ignorance and disbelief) and We gave him life (by knowledge and Faith) and set for him a light (of Belief) whereby he can walk amongst men, like him who is in the darkness (of disbelief, polytheism and hypocrisy) from which he can never come out?] [Surah Al-An’aam Aayah 122]
The first person is a believer who is [given insight, clear guidance etc] through the light of Eemaan, love of Allaah, knowledge and awareness of Allaah and remembrance of Allaah. The second person is a heedless person who is heedless of Allaah, turns away from remembrance of Allaah and love of Allaah. [Indeed], absolute success is [achieved as a result of the] light of [Eemaan, Allaah’s guidance etc] and absolute wretchedness [befalls a person as a result of] missing this light. And due to this, the Prophet [sallal-laahu-alayhi-wasallam] used to ask Allaah: “O Allah! place light in my heart, light in my hearing, light in my sight, light on my right, light on my left, light in front of me, light behind me, light above me, light below me, make light for me.’’ [Muslim 763] Dhikr is a light for a person’s face and body parts, light for him in his worldly [affairs], in the grave and on the day of resurrection.
 From the benefits of Dhikr is that [by way of a it], a person earns [Allaah’s blessings, forgiveness, praise and benevolence] and the angels [supplicate for him and ask Allaah to forgive him]. And whoever [receives this from] Allaah and the angels, then indeed he will be successful. Allaah said:
يَـٰٓأَيُّہَا ٱلَّذِينَ ءَامَنُواْ ٱذۡكُرُواْ ٱللَّهَ ذِكۡرً۬ا كَثِيرً۬ا
وَسَبِّحُوهُ بُكۡرَةً۬ وَأَصِيلاً
هُوَ ٱلَّذِى يُصَلِّى عَلَيۡكُمۡ وَمَلَـٰٓٮِٕكَتُهُ ۥ لِيُخۡرِجَكُم مِّنَ ٱلظُّلُمَـٰتِ إِلَى ٱلنُّورِۚ وَڪَانَ بِٱلۡمُؤۡمِنِينَ رَحِيمً۬ا
O you who believe! Remember Allaah with much remembrance. And glorify His Praises morning and afternoon [the early morning (Fajr) and ‘Asr prayers]. He it is Who sends [blessings, forgiveness, praise and benevolence] on you, and His angels too [supplicate for you and ask Allaah to forgive you(Ref2)], that He may bring you out from darkness [of disbelief and polytheism] into light [of Belief and Islamic Monotheism]. And He is Ever Most Merciful to the believers. [Surah Al-Ahzaab. Aayaat 41-43] [Fiqhul Ad-iyah Wal Ad-kaar. pages 17-21. sections 1 & 2. slightly paraphrased]
Refs 1 & 2: Source: Zaadul Maseer Fee Ilmit Tafseer- By Imaam Ibnul Jawzi [rahimahullaah]