To what extent is it obligatory to supplicate for Muslims, and is a Muslim sinful if he does not supplicate for someone who is in need of supplication?

A Muslim should supplicate for himself, his brethren, and all Muslims. Allah has praised the believers who supplicate for past and future Muslims. The generalization of supplication is emphasized when the supplicator is an Imam or a Khatib, because if he dedicates the supplication to himself alone, he has betrayed them. The Prophet (peace be upon him) encouraged supplicating for one's brethren. If a Muslim is alone or supplicating secretly, he may supplicate for himself exclusively, but it is better to include his brethren and the generality of believers in his supplication, recognizing that Muslims are like one body. The supplications in the Qur'an are in the plural form to draw attention to the virtue of including one's brethren in supplication.