It is forbidden and is not permissible to play musical instruments or listen to songs and tunes. The majoritity of scholars say that it is haraam, including the four imams of fiqh: Abu Haneefah, Maalik, Al-Shaafa'i and Ahmad (may Allah have mercy on them all).
Evidence of prohibition in the Quran and Sunnah:
Allah says in Surah Luqmaan " And of mankind is he who purchases idle talks (i.e. music, singing) to mislead men from the path of Allah..." (Quran 31:6)
Al-Hasan Al-Basri (May Allah have mercy on him) said: this aayah was revealed concerning singing and musical instruments (lit. woodwind instruments). (Tafseer Ibn Katheer, 3/451).
Allah says in the Quran: [Allah said to Iblees] " And befool them gradually those whom you can among them with your voice (i.e songs, music and any other call for Allah's disobedience).." (Surah Al-Israa 17:64)
The scholars therefore say that everyone who speaks in any way that is not obedient to Allah, everyone who blows into a flute or other woodwind instrument, or who plays any haraam kind of drum, this is the voice of the Shaytaan.
Yusuf Islam was at the GPU event yesterday where he performed his new song playing a guitar and he explained that he now follows another school of thought (which i think he said originates from Baghdad) that states that music is not haraam, he went on to say that no one should judge him but Allah which is the truth.