There does not exist a word in English that can serve as an equivalent to the Arabic word (مجاهد, mujāhid; nominative plural: مجاهدون, mujāhidūn; oblique plural: مجاهدين, mujāhidīn).
Who or what is a mujāhid? I’m glad you asked. It means, literally, one who performs (جهاد, jihād), especially what is termed (جهاد بالسيف, jihād bi-s-sayf, jihad with/by the sword) or (جهاد في سبيل الله, jihād fi sabīlillāh, or jihad in the path of God). This means, in other words, one who fights for God/Islam. And this fighting is not of the spiritual sort but, rather, of the military and armed sort.
Some have taken to calling these people “jihadis”. This is not incorrect or inaccurate: in Arabic (as well as other languages, such as Persian and Urdu), (جهادي, jihādī) means not only “of or pertaining to jihad” but also “supportive of or belonging to jihad”, which can be used to describe the many sorts of people who conduct jihad or support it. But how much of this do the normal people know? To how many would it be a strange word or one devoid of meaning or connotation?
Despite the many parallels drawn between the two, mujāhidūn or jihad-fighters or jihadis are not Crusaders or even like them. Jihad-fighters wage war unprovoked. Or, rather, one’s infidel-hood is sufficient provocation to cause them to wage war. (A completely different issue, of course, is why we in the West continue to condemn the Crusades while failing to condemn or, even worse, overlooking the Islamic/Islamist wars of conquest.)
The round-about descriptive way is to refer to such people as “militant Islamist terrorists” (while their supporters are “militant Islamists” or somesuch). But this becomes a mouthful. But it does preserve an element I believe is key: putting this terrorism issue in the context of Islamism. Terrorism is but a manifestation of Islamism, not the other way around. And yet I fear that using such terms can only open the door for endless symantic debates as well as seeming to be fearful of offending someone. (“Islamo-fascists” is quite more assertive and strident than “militant Islamist terrorist networks et cetera“.)
Of course Arabic would have the perfect word, what with its hundreds of permutations for a single root. Applying its own rules in the same manner, so would Hebrew. But then none of us speak Hebrew, so that would not help us.