What is the ruling on personal use of non-free programs, such as file-downloading programs, knowing that some of these files may be given to others, such as audio and software files?

As long as the owners of the files prevent their free download and copying, it is not permissible to infringe upon them without their permission, because these are rights protected by Islamic law. The Islamic Fiqh Academy has resolved that copyrights and intellectual property rights are protected by Islamic law and it is not permissible to infringe upon them. The most cautious and absolving approach is not to copy or download them. If personal use is prohibited, then it is even more so prohibited to give them to others.