I have heard many traditions concerning reciting the Noble Quran and I know it has much thawab if we recite it. For instance, there is a narration from the apostle of Allah (pbuh) that said:

Whoever recites a letter from the Holy Quran, it will be written for him a Hassanah that 10 times has more thawab… .(Majma'ul Bayan Page36)

Or in another tradition, the Prophet (peace be upon him and his household) said:

the best Ebadah of my Ummah is reciting of the Quran. (Wasaelul-Shia, Vol.6, Pg.168)

But I wonder if it is mandatory (Wajib) for a Muslim to recite it or it is just as a recommended practice (except reciting the Quran during the salah)