Associating other deities with Allah is the one unforgiveable sin in Islam.
Allah T'ala says in the Holy Quran:
إِنَّ اللّهَ لاَ يَغْفِرُ أَن يُشْرَكَ بِهِ وَيَغْفِرُ مَا دُونَ ذَلِكَ لِمَن يَشَاء وَمَن يُشْرِكْ بِاللّهِ فَقَدِ افْتَرَى إِثْمًا عَظِيمًا
004.048 God forgives not that partners should be set up with Him; but He forgives
anything else, to whom He pleases; to set up partners with God is to devise a sin
Most heinous indeed.
The purpose of this verse is not to tell man that he may commit any sin as long as he does not associate others with God in His divinity. The object is rather to impress upon those who had begun to regard polytheism as a trivial matter that it constitutes the most serious offence in God's sight, an offence so serious that while other sins may be pardoned this will not.
The Arabic word Shirk can be translated as polytheism. Polytheism should be understood in the light of the Islamic Holy texts.
Shirk is that people should associate none with God in His divinity: neither in His essence, nor in His attributes, nor in His powers and authority, nor in the rights He has against His creatures.
To associate someone with God in His divinity is to declare that the former shares the essence of God's divinity. Instances of associating others in God's essence are the Christian doctrine of the Trinity, the belief of the pagan Arabs that angels are daughters of God, and the belief of other polytheists in the divine character of their self-styled gods and goddesses and, in some cases, of their royalty.
Likewise, a person associates others in the attributes of God when he considers someone other than God to be invested with those attributes which belong exclusively to God. One becomes guilty of this kind of polytheism if one believes somebody either to know all the mysteries of the Unseen or to be all-seeing and all-hearing or to be free of all defects and weaknesses and thus infallible.
A person associates others in the authority of God when he recognizes someone to be possessed of authority which belongs to God alone by virtue of His godhead; for example, the power to either benefit or harm people in a supernatural manner, to fulfil the needs of people and rescue them from distress, to protect and shield them, to hear their prayers, to make or mar their fate. A person is guilty of the same when he recognizes someone as possessing the rightful authority to determine what is lawful and what is unlawful, and to make laws for the regulation of human life. Such authority belongs to God alone, and recognizing anyone other than God as possessing it is tantamount to associating others with God in His authority.
Moreover, to associate others with God in His divine rights means that one recognizes someone beside God as legitimately deserving that which may he asked of man by God alone, viz. bowing and prostrating, standing in awe and reverence with folded hands, devotional greeting and kissing the earth, slaughtering animals and making any other offerings in thanksgiving for his grace and benevolence and in acknowledgement of his overlordship, vowing offerings in his name, calling him to rescue one from one's affliction and misfortune, and all the other forms of worship, adoration and reverence which are exclusively for God. In the same way, no one has the right to be loved to the exclusion of all other attachments, or to be held in such awe that one always fears his wrath and dreads the violation of his command, both openly and in secret. Likewise, it is God - and God alone - Who has the right to be obeyed unconditionally, and Whose guidance should be considered the only criterion of right and wrong. In the same way, man should not commit himself to obey any authority which is either independent of obedience to God or whose command lacks the sanction of God.
If someone accords any of these rights to anyone other than God, he is guilty of associating others with God in His divinity. His guilt is the same whether or not he calls such beings divine. (Tafheemul Quran)