Is allowed to copy CD's or video tapes because the originals are very expensive? It is very helpful, especially if it is for non-Muslim companies, eg: CD's teaching computer skills.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Recording computer programs videos or others is forbidden unless permitted by their owner. Here is the Fatwa of the permanent council of Fatwa in Saudi Arabia:
"It is unlawful to make copies of programs whose rights are reserved to their owners except with the permission of these owners. The Prophet said:"Muslims are bound by the conditions they set amongst themselves". [Al Hakeem]
The Prophet also said: "Nobody is permitted to take the property of a Muslim unless the Muslim permits him voluntarily to do so". [Al Daraqutny].
The Prophet also said: "Whoever takes hold of a lawful thing before others, he has more right to possess it than others" [Abu Dawood].
So, it is forbidden to copy these programs without the permission of their owners regardless of their being Muslims or non-Muslims.
So, if the owner of these programs forbids only public copying and allows private one, the person can copy the program for private use as stipulated. But if he forbids both public and private copying it becomes then absolutely forbidden to copy these programs. Some companies put a sign meaning, "I swear not to abuse your program or use an unauthorized copy of it". So, if the person does not comply with his oath that is a major sin which could lead one to being thrown in Hell-fire.
Allah knows best.