From the Fatawa of Shaykh 'Abd al-Halim Mahmud: 

Abu Bakr al-Kattani stated in his definition of Sufism (al-Tasawwuf) that it consists of [high-quality] comportment (khuluq).  So one whose comportment improves in quality, his purity (al-safa') will [similarly] become increased.  

Abu al-Hasan al-Nawawi stated, "Sufism neither consists of particular customs nor knowledge.  Rather it consists of [high-quality] comportment (khuluq).  Were it to consist of particular customs, it could be attained thorugh striving (al-mujahada); and were it to consist of knowledge, it could be attained through instruction.  Sufism, however, consists of taking on the qualities of God (akhlaq Allah).   

Shibli defined it [Sufism], saying that its beginning is gnosis of God; and its end point is His affirmation of unity.   

And the comprehensive definition is the words of Abu Bakr al-Kattani, Sufism is purity and witnessing. And Sufism began immediately with [the advent of] Islam.  This is because Islam consists of noble behavior as well as attunement to God in both simple affairs and those of great magnitude. 
  
Among the first Sufis after the Companions [of the Prophet] and the Followers [who succeeded them] were Ibrahim ibn Ad'ham and Fudayl ibn 'Ayyad.  As a consequence of people's confusion between the [terms] ascetic (zahid), worshipper ('abid), and Sufi, we can state [the following]: 

The ascetic is one who turns away from the goods of the world and its pleasant things. 

The worshipper is one who is careful to observe the acts of worships, such as getting up [to prayer at night] (al-qiyam), canonical prayer (al-salat), and similar things. 

The Sufi is both an ascetic and a worshipper.  Thus the Sufi abstains from the world, since he is beyond the point where anything can distract him from God.   

Also, the Sufi is a worshipper because of his constancy with God and his link with God (may He be exalted).  He worships God because God is suitable for worshipping, not out of desire or fear.  [The Sufi woman saint] Rabi'ah al-'Adawiya --may God be pleased with her-- said, "O God, if I am worshipping you out of fear of Your hellfire, cast me into it.  And if I am worshipping you out of desire for Your paradise, prohibit me from entering it.  And if I am worshipping  You for the sake of Your noble face, do not prohibit me from seeing You."