Short answer
Sufism (tasawwuf) in its true sense is not haram: it is the work of purifying the heart, which the hadith calls ihsan, worshipping Allah as if you see Him. Mainstream Hanafi and Deobandi scholars accept tasawwuf that stays within the Quran and Sunnah, and reject any practice or belief that breaks the Shariah, whoever does it.
Deobandi scholars such as Mawlana Ashraf Ali Thanawi taught tasawwuf as the inner side of the Shariah: sincerity, humility, remembrance of Allah and struggle against the ego, often with a qualified teacher. Practices that break the Shariah, such as prostrating at graves, musical gatherings, or claiming that a spiritual path frees a person from prayer, are rejected.
The four schools agree on this.
Explanation
In the hadith of Jibril the Prophet ﷺ defined three levels of the religion: Islam (the outward acts), iman (belief), and ihsan, "to worship Allah as if you see Him, and if you do not see Him, He sees you." The Quran says "He has succeeded who purifies it, and he has failed who instills it [with corruption]" (91:9-10). Purifying the soul of pride, envy, showing off and love of the world is a duty on every Muslim. Tasawwuf, at its core, is the science of doing that.
The early masters of this path, such as al-Junayd, taught that it is bound by the Quran and Sunnah, and that anyone who has not learned them should not be followed in it. That is the measure: a true Sufi teacher follows the Shariah more carefully than others, prays on time, keeps the Sunnah and teaches people to do the same. Taking a shaykh (bay'ah) is a means many find helpful, not an obligation.
Over the centuries, practices spread under the name of Sufism that many scholars, including Sufi scholars themselves, rejected: seeking help from the dead in ways that compromise tawheed, dancing and music at gatherings, and claims that a saint is above the law. Some respected scholars, especially from the Salafi tradition, are wary of the label itself for this reason. The fair position is to judge practices by the Quran and Sunnah rather than by the name.
For related questions see does Islam have saints?, is tawassul allowed? and Islamic meditation (muraqabah).
The evidence
Quran, Surah Ash-Shams 91:9-10
قَدْ أَفْلَحَ مَن زَكَّىٰهَا ﴿٩﴾ وَقَدْ خَابَ مَن دَسَّىٰهَا ﴿١٠﴾
He has succeeded who purifies it, And he has failed who instills it [with corruption].
Shows that purifying the soul is the path to success.
Sahih al-Bukhari 50
Sahih... أَنْ تَعْبُدَ اللَّهَ كَأَنَّكَ تَرَاهُ، فَإِنْ لَمْ تَكُنْ تَرَاهُ فَإِنَّهُ يَرَاكَ ...
"To worship Allah as if you see Him, and if you do not see Him, He sees you."
Defines ihsan, the goal of tasawwuf.
Where the ruling is recorded
- Shariat and Tariqat (Mawlana Ashraf Ali Thanawi), Discussion of the relation between the Shariah and the spiritual path. Explains that the path is the inner side of the Shariah and cannot contradict it.
- al-Risala al-Qushayriyya (al-Qushayri), Introduction and the biographies of the early masters. Records the early teachers' insistence on following the Quran and Sunnah.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.