Is it permissible to listen to the adhaan at times other than the times of prayer?
There does not seem to be anything wrong with listening to the adhaan at any time, other than the times of prayer. In the adhaan there is remembrance of Allah, glorification of Him and other noble meanings.
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said:
Al-Qurtubi and others said: The adhaan, although its phrases are few, includes issues of ‘aqeedah (belief), because it starts with takbeer (“Allahu akbar”), which speaks of the existence and perfection of Allah; then it praises Him and proclaims His Oneness (Tawheed) and denies that He has any partner; then it affirms the Messengership of Muhammad (blessings and peace of Allah be upon him); then it calls to obedience following the testimony that Muhammad (blessings and peace of Allah be upon him) is the Messenger of Allah, because how He is to be obeyed can only be known through the Messenger; then it calls to success, which is eternal life, which is a reference to the resurrection; then it repeats phrases by way of affirmation.
Fath al-Baari, 2/77.
Based on that, there is nothing wrong with listening to the adhaan in programs or mobile phones or recorded tapes and so on, whilst pondering noble meanings that this call contains.
But we should point out that when listening to the adhaan in these ways, it is not prescribed to repeat its phrases.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: If the adhaan is recorded and is not being given at the time of prayer, then its phrases do not have to be repeated, because this is not a real call to prayer, i.e., it is not being given when it is enjoined to give it; rather it is a recording of a previous call to prayer.
Majmoo‘ Fataawa al-Shaykh al-‘Uthaymeen, 12/196
And Allah knows best.