There are are a number of ahaadeeth that show us the virtue of isti'aadhah:
(1) Imaam al-Bukhaaree رحمه الله reports on the authority of Sulaymaan Ibn Sarad رضي الله عنه that, "Two men abused each other in the presence of the Prophet صلى الله عليه وسلم while we were sitting with him. One of the two abused the other while in a state of rage, and his face turned red. The Prophet صلى الله عليه وسلم said, 'I know a statement that if he were to say, what he is experiencing would leave him. If only he were to say, "I take refuge with Allaah from the accursed Shaytaan (a'oothu billaahi minash-shaytaanir-rajeem)."'" 
(2) Imaam Ahmad رحمه الله reports on the authority of Abu Dharr رضي الله عنه that the Messenger of Allaah صلى الله عليه وسلم said, "O Abu Dharr! Take refuge with Allaah from the Shayaateen amongst men and jinn." Abu Dharr رضي الله عنه asked, "Are their Shayaateen amongst men?" The Prophet صلى الله عليه وسلم replied, "Yes." 
(3) Imaam Abu Daawood رحمه الله reports on the authority of Ibn 'Abbaas رضي الله عنهما that the Messenger of Allaah said, "If anyone seeks refuge [with you] for the sake of Allaah سبحانه و تعالى then grant him refuge. If anyone asks of you for the sake of Allaah سبحانه و تعالى then grant his request." 
(4) Imaam at-Tirmidhi رحمه الله records on the authority of Ma'qal Ibn Yasaar رضي الله عنه that the Messenger of Allaah صلى الله عليه وسلم said, "Whoever says, 'A'oothu billaahis-Samee'il-'Aleem' [one narration adds, 'minash-shaytaanir-rajeem] three times upon awakening and then recites the last three verses of Sooratul-Hashr, Allaah will appoint seventy thousand Angels over him to invoke blessings upon him until he goes to sleep. Were he to die on that day he would have died as a martyr. Whoever says this when he goes to sleep, the same holds true." 
(5) Imaam Muslim رحمه الله records on the authority of Ummul Mu'mineen 'Aa'ishah رضي الله عنها that the Prophet صلى الله عليه وسلم used to say, "I take refuge with Your pleasure from Your displeasure; I take refuge with Your forgiveness from Your punishment; I take refuge with You from You." 
Imaam Ibn al-Jawzee رحمه الله said, "Know that the one who is taking refuge with Allaah, the Great, from the accursed Shaytaan  has clung to the firm Rope of Allaah. I take refuge with Allaah from all sins and actions of transgression! I take refuge with Allaah from misguidance and treachery! I take refuge with Allaah from the displeasure of ar-Rahmaan!
O my brother! Know that when the servant clings to the rope of the created king, he is saved from the evil of the oppressors. Therefore, it is far more befitting and appropriate for the one who takes refuge with the Lord of the Universe from the accursed enemy, Shaytaan, that he be saved."