Indeed, Allaah has forbidden the Muslims from fornication and all the pathways, which lead to it. He (T) has said (which means):

"And do not come near zinaa (fornication)! Indeed, it is an abomination, and an evil way."
(Al-Israa': 32)

Among the many things that excite passions between a man and a woman, is touching. Thus, touching, which opens the door to fornication, is also forbidden as it is a form of fornication, since the Prophet (S) said:

The eyes fornicate. Their fornication is the (illegal) look. The hands fornicate. Their fornication is the touch. The feet fornicate. Their fornication is the walking (towards a woman). The heart desires, and the private parts either confirm it or deny it. (Al-Bukhaaree)

Unfortunately, some form of this type of fornication is unavoidable. Although, we may not commit the indecent sexual act itself, indeed, our eyes, our hands, and our feet fornicate at least once in our lives. There is no doubt about that, as the Prophet (S) said:

Every one of the sons of Aadam has his share of fornication written for him. (Al-Bukhaaree)

Therefore, we must try our best to avoid fornication and every pathway leading to it. Since the hand has the capability of fornicating, then it is forbidden for the woman to touch a man that is not a mahram to her. A mahram is someone that the Muslim woman is permitted to uncover (her veil) in front of. They consist of her father, husband, brother, mother's brothers, father's brothers, and all the others mentioned in Sooraat an-Noor: 31 in the Qur'aan. We shall present a brief look at the evidences prohibiting non-related men and women from touching each other, from three perspectives:

The Warning from the Prophet (S)

The Prophet (S) said:

It is better for a spike to be driven into your head than for you to touch a woman that is not permissible for you (to touch). (Recorded by at-Tabaraanee in al-Kabeer)

According to the above narration, we can plainly see the prohibition of a man touching a woman. Although the Prophet (S) did not directly command the Muslims to not do it, his statements show the severity of the consequences of committing such an act. If it were allowed to touch non-related men and women, then the Prophet (S) would not have spoken so drastically of the one who does so. Consequently, it is forbidden for the man to touch any woman that he is not a mahram for, as well as a woman to touch any man that is not a mahram to her. This is the opinion that the majority of the scholars have taken and it is the truth of which there is no doubt.

Ahmad Bin Hanbal (r) said:

"The specified look at women-strangers, as well as touching them is forbidden."(Al-Muntahaa)

Commenting on the hadeeth, al-Albaanee said:

"In this hadeeth, there is a severe threat to he who touches a woman that is not permissible for him. In it is also a proof for the prohibition of shaking hands with women, because that entails touching without a doubt. "(As-Saheehah: no. 226)

Apart from the above-mentioned men, the Muslim woman is not allowed to touch any man whether Muslim or non-Muslim. If she does so then she has fallen into sin and commenced on one of the many pathways toward fornication. And we seek Allaah's refuge from that!

Arguments

Although the above evidences and ruling based on such, may seem clear and evident, some raise arguments which may seem contradictory to what is established. However, they do not present a contradiction, and will be answered:

No Prohibition

Someone may say, "The Prophet (S) did not directly prohibit not touching women. His not doing so is only his
Sunnah (example) and something only for him."

The claim that he (S) did not prohibit it, is a claim that could only be made by those who lack the knowledge of basic fiqh pricnibles. It is through these princibles that we understand how to apply Allaah's legislation. Among these basic princibles are the following;

1. Something is obligatory to avoid, if not doing so would incurr the commission of something prohibted. He (S) said;

It is better for a spike to be driven into your head than for you to touch a woman that is not permissible for you (to touch).

So avoiding "touching a woman" is obligatory, since it is worse that driving a spike into your head. So such a naive statment implies the following; "The Prophet (S) did not prohibit driving a spike into one's own head, rather, he only avoiding doing it as a Sunnah that was particular to him."!!!?

2. The usage of the statment "not permissible" implies "not permissible", unless there is a text to clarify that it is only disliked or abrogated, etc.

Ambiguity

One may say, "The hadeeth is not clear, since the word used for touch (massa) can either mean a touch with sexual desire or a touch without desire. Therefore, a touch with no lust involved is allowed (i.e. with an old man)."

This would be a possibility if there were conflicting texts, which is not the case here. For example, does touching the private part break wudhu' or not. Some narrations say, "It is part of him", whereas another says that it requires wudhu'. In this case, when two texts coincide, harmonization must be made, or abrogation must be demonstrated. So then this claim is a possibility. But on the other hand, passing wind breaks wudhu', weather it is done out of pleasure or not, and no one claims otherwise, and this is because there is no text to require that!

Not In The Qur'an

One may claim, "The command for not touching is in a hadeeth and not in the Qur'aan. Therefore, Allaah has not prohibited it.".

There are many texts to prove that the one who disobeys the Messenger has disobeyed Allaah. Therefore, when a person says this, it is more important for them to repent from the disbelief that they have expressed than to be concerned with the issue that we are discussing. Indeed saying a statement of kufr like this one, and believing in it, is worse than having a spike driven in one's head. Therefore we can only say as Allaah has said to Muhammad (S);

"Then if they disobey you, say, "Indeed I am innocent of what you do."" (Ash-Sha'raa' 26:216)

This is a two step process, first innocence is claimed, and then;

"So they disobeyed the Messengers of their Lord, so He punished them all with abounding destruction." (Al-Haaqah 69:10)

Then all of those who disobey the Messenger (S) are destroyed, either in this life or the Hereafter. So indeed this is a matter much worse than a spike in the head.

The Rule of Necessity

It is allowable for a man to touch a woman not related to him in the case of emergency, such as when a woman has no option but to be treated by a male-doctor, and she is in dire need of treatment, or when there is a life-or-death emergency. These examples fall under the rule of necessity.