Both Sunni and Shi'i hadith speak about ruqya, or the treatment of medical or metaphysical problems (such as the evil eye or jinn-related problems), through recitation of Qur'an.
For Shi'i hadith, you could consult Wasa'il al-Shi'a, vol. 6, book 41. ("On the permissibility of ta'widh, ruqya, and nashra").
This seems to have been a common practice among Muslims in classical times, similar to some aspects of traditional medicine.
However, today, this is more commonly emphasized and practiced by Sunnis. Sunnis speak about it a lot more, whereas the subject is mostly absent from formal Shi'i discourse. (Of course, this varies from culture to culture.)
As for the views of individual Muslims, Sunni or Shi'i, people tend to have a wide range of personal views about matters such as spiritual healing and the unseen.
Insofar as techniques for ruqya that are used in practice sometimes extend well beyond the recitation of Qur'an, individual Sunni and Shi'i scholars may also have varying opinions on what techniques are acceptable or not.
However, the basic idea is present in both Sunni and Shi'i hadith.