Praise be to Allah.
The Permanent Committee for Iftaa' (Islamic Rulings), chaired by Sheikh Abdul-Aziz bin Baz, has replied to this question by ruling that it is not permissible to copy software without permission from the original author or the copyright holder based on the following three haadeeth of the Prophet (peace be upon him):
(1) "Muslims are to honor their agreements (with others)";
(2) "A Muslim's wealth is forbidden for others to use without his permission;" and,
(3) "Whoever is the first to acquire a mubaah (something lawful to acquire) is entitled to keep it". This applies to both Muslims and non-believers (who are not engaged in an act of war with Muslims) because the right of a non-believer is respected in the same manner as a Muslim's right. Allah knows best. (Committee Fatwa no: 18453)
Also, Sheikh Muhammad bin Salih Al-'Uthaimeen has ruled that whatever is customary among people should be the rule except when a user wants a copy for himself and the author or the copyright holder did not explicitly prohibit copying the software for private or public use. However, if the author or the copyright holder specifically stated that private and public copying of the software is prohibited, then it is not permissible to copy that software.