Allaah سبحانه و تعالى says,
A group of reciters and scholars, from amongst them Imaam Hamza رحمه الله, Imaam Ibn Seereen رحمه الله, Imaam Ibraaheem an-Nakha'ee رحمه الله and Imaam Daawood adh-Dhaahiree رحمه الله, were of the opinion that one seeks refuge after the completion of recitation, taking to the literal sense of this verse. They also stated that the reason for doing so would be to repress self-astonishment at the completion of an act of worship.
A second opinion voiced is that one seeks refuge before and after the recitation. However, the famous and well-known opinion, which is the opinion of the majority, is that one seeks refuge before recitation in order to safegaurd oneself from the whisperings of Shaytaan.
This group understood the meaning of the verse to be, 'When you wish to read the Qur'aan...' in the same sense as the verse,
Imaam Abu Daawood رحمه الله records on the authority of Abu Sa'eed al-Khudree رضي الله عنه that, "When the Messenger of Allaah صلى الله عليه وسلم stood at night [for prayer, he would commence the prayer] by saying the takbeer and then saying, 'SubhaanakAllaahumma wa bihamdika, wa tabaarakasmuka, wa ta'aalaa jadduka, wa laa ilaaha ghayruk (You are glorified O Allaah and praised! Your Name is Blessed; Your Majesty Exalted and none has the right to be worshipped save You).'"
Then he would say, "Laa ilaaha illAllaah (There is none worthy of worship except for Allaah)," three times, then he would say, "Allaahu Akbar (Allaah is the greatest)," three times and then he would say, "A'oothu billaahis-Samee'il-'Aleem minash-Shaytaanir-Rajeem, min hamzihee wa nafkhihee wa nafthih (I take refuge with Allaah, the All-Seeing, the All-Knowing from the accursed Shaytaan; from his madness, arrogance and poetry)." 
Imaam Abu Dawood رحمه الله also reports on the authority of Naafi' Ibn Jubayr رحمه الله, from his father who said, "I saw the Messenger of Allaah صلى الله عليه وسلم saying when he commenced the prayer, "Allaahu Akbar kabeera (Allaah is the greatest, very great)," three times, "Alhamdulillaahi katheera (Abundant praise and thanks be to Allaah)," three times and "SubhaanAllaahi bukratan wa aseela (Glorified be Allaah, morning and evening)," three times. Then he said, "Allaahumma innee a'oothubika minash-Shaytaanir-Rajeem, min hamzihee wa nafkhihee wa nafthih (I take refuge with Allaah, the All-Seeing, the All-Knowing from the accursed Shaytaan; from his madness, arrogance and poetry)." 
Imaam ash-Shaafi'ee رحمه الله and Imaam Abu Haneefah رحمه الله were of the opinion that the wording of the isti'aadhah should be, "A'oothu billaahi minash-Shaytaanir-Rajeem," such that it conforms to the aforementioned verse in Sooratun-Nahl. Imaam Ahmad رحمه الله said that is was most befitting to say, "A'oothu billaahi minash-Shaytaanir-Rajeem innahoo huwas-Samee'ul-'Aleem," such that the person combines the wording of the verse in Sooratun-Nahl and Soorah Fussilat. Some of the Shawaafi' said that one should say, "A'oothu billaahis-Samee'il-'Aleem minash-Shaytaanir-Rajeem," to conform to the hadeeth of Imaam Abu Daawood رحمه الله and also to combine the wording of both verses.
The majority of the scholars are of the opinion that isti'aadhah is recommended and not obligatory. However, it is reported from Imaam 'Ataa' Ibn Abi Rabaah رحمه الله that it is obligatory to say it within the prayer and outside the prayer when one desires to recite the Book of Allaah سبحانه و تعالى. Imaam ar-Raazee رحمه الله stated that the proof for this opinion was that the verse, "Seek refuge with Allaah," is mentioned in the imperative, that the Messenger of Allaah صلى الله عليه وسلم persisted in uttering it throughout his life, and that it serves as a protective barrier from Shaytaan - therefore if an obligation can only be fulfilled by a particular means, that means also becomes an obligation.