The holy Qur`an constitutes the words of Allah the Almighty which He revealed to the best of His messengers and creations, our master Muhammad . Allah commands us to respect the Qur`an, venerate it and handle it in a manner that dignifies it above everything else. None must touch the mus-haf (copy of the Qur`an) except one who is purified from both major and minor ritual states of impurity. Allah says,

Indeed, it is a noble Qur'an. In a Register well-protected; none touch it except the purified. [Al-Waqi'a: 77-79]

It is impermissible to place any book over a mus-haf because it is exalted and nothing should be placed on it. The superiority of the words of Allah over other words is like the superiority of Allah over His creatures. Therefore, it is inappropriate and disrespectful to set the Qur`an in place of mobile ringtones. This is because the sanctity and sublimity of the Qur`an elevate it above such uses. Allah says,

And whoever honors the symbols of Allah - indeed, it is from the piety of hearts. [Al-Hajj: 32]

Using verses of the holy Qur'an in place of mobile ringtones is tantamount to abusing the sanctity of the holy Qur`an which Allah revealed for remembrance and worship through its recitation. The Qur`an was not revealed to be misused in such a way as to debase its verses or remove it from its legal purpose. 

We are commanded to contemplate the verses of the Qur`an and fathom the meanings of its words. Using it in place of ringtones removes it from this legal purpose to the level of the mundane such as a mere telephone call. This drives one's attention away from contemplating its meanings to answering calls in addition to interrupting the verses and severing their meanings — sometimes even their inversion —upon stopping the recitation to answer the call.

Likewise, it is improper to set the adhan as a mobile ringtone. The adhan was legislated to inform of the time of prayer and using it as a ringtone creates confusion, causing people to mistakenly assume that the time of prayer has entered. Furthermore, it involves inappropriately using it for purposes other than that for which it was prescribed.  A person can—if he so wishes—instead use Islamic songs or prophetic eulogies that are suited to the short duration of ringtones. Allah's words are sacred and must be treated accordingly.

Allah the Almighty knows best.