If singing is accompanied by musical instruments then it is haraam to do it or to listen to it, whether it is done by a man or a woman. The only exception that is made is singing that is accompanied by the daff, done by women at weddings or on Eid, and when one who has been absent returns. We have already discussed this in detail in the answer to question no. 5000 and 20406. 

With regard to religious songs, if they are accompanied by music (with instruments) or if they are sung by a woman to men, then they are haraam, and calling them religious songs in this case is calling something by a name other than its real name in order to confuse and deceive people so that they will accept it. How can they be religious songs when Allaah and His Messenger (peace and blessings of Allaah be upon him) have forbidden them? 

If they are free of musical accompaniment, and are done by a man and contain good and beneficial meanings, then they are permissible, but one should not listen to them too much. 

The Standing Committee issued a detailed fatwa on the topic of Islamic nasheeds, which says the following: 

You are correct in saying that songs in the current form are haraam because they include bad words and things in which there is no good; indeed they comprise idle speech, provocation of desires, indecent meanings and tempting voices. May Allaah help us and you to do all that is good. 

It is permissible for you to replace these songs with Islamic nasheeds which contain words of wisdom and exhortation and lessons, which promote keenness to follow Islam and invoke Islamic feelings, which put one off evil and the things that promote it, and which motivate the one who “sings” them and the one who hears them to obey Allaah and discourage them to disobey Him or transgress His limits; they make one keen to protect His sharee’ah and strive in jihad for His sake. But you should not take that as a habit which one persists in, rather that should be something that is done only sometimes, on special occasions such as weddings or when travelling for jihad and so on, and when one feels low, in order to revive the spirit and motivate oneself to do good, or when one feels inclined towards evil, so listening to such nasheeds may ward that off. 

What is better than that is to take a portion of Qur’aan to recite, and a wird of saheeh dhikrs, for that is more purifying for the soul and is better for bringing peace of mind. Allaah says (interpretation of the meaning): 

“Allaah has sent down the Best Statement, a Book (this Qur’aan), its parts resembling each other (in goodness and truth) (and) oft‑repeated. The skins of those who fear their Lord shiver from it (when they recite it or hear it). Then their skin and their heart soften to the remembrance of Allaah. That is the Guidance of Allaah. He guides therewith whom He wills; and whomever Allaah sends astray, for him there is no guide”

[al-Zumar 39:23]

“Those who believed (in the Oneness of Allaah — Islamic Monotheism), and whose hearts find rest in the remembrance of Allaah verily, in the remembrance of Allaah do hearts find rest.

29. Those who believed (in the Oneness of Allaah — Islamic Monotheism), and work righteousness, Tooba (all kinds of happiness or name of a tree in Paradise) is for them and a beautiful place of (final) return”

[al-Ra’d 13:28, 29]

It was the habit of the Sahaabah (may Allaah be pleased with them) to focus on the Qur'aan, memorizing it, studying it and acting upon it. However they also had nasheeds and chants that they would “sing”, such as when they were digging the Ditch (al-khandaq) and when building mosques, when travelling for jihad and on other such occasions, without making that their symbol or paying too much attention to it. Rather it was something in which they would occasionally find relaxation and stir up positive feelings. With regard to the drum (tabl) and other kinds of musical instruments, it is not permissible to use them with these nasheeds, because the Prophet (peace and blessings of Allaah be upon him) and his companions (may Allaah be pleased with them) did not do that. And Allaah is the Guide to the Straight Path; may Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. 

Fataawa Islamiyyah, 4/532. 

With regard to hearing songs and music without intending to and without listening attentively to them, such as when a person hears them in a store and so on, there is no sin on him. What is forbidden is listening, not just hearing. But he must also try to advise others against doing evil actions. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: As for simply hearing without intending to or listening attentively to them, such as when a person who is walking down the street hears the sound of songs coming from shops or passing cars, or when he is in his own house and hears songs coming from his neighbours’ houses without wanting to hear it, in such cases he has no control over the situation and there is no sin on him. But he should advise others and speak out against this evil with wisdom and beautiful preaching, and he should strive to avoid it as much as possible. And Allaah does not burden any person beyond his scope.  

Fataawa Islamiyyah, 4/389 

And Allaah knows best.