It is my understanding that the default position within mainstream Christianity is that prayer and reading the Bible are key to promoting spiritual well-being and growth and that as such they are extremely important for growing in faith and maintaining it. However, I was wondering if any denominations obligate (by which I mean set as the rule for life in a similar fashion to prayer in mainstream Islam) daily prayer and Bible reading? Conversely are there any actively discourage daily prayer and/or daily Bible reading?
Disclaimer: I am unsure whether this answer fits your intended meaning of "mandatory" or "obligatory".
LDS members are taught they should have daily scripture study and prayer. In fact, in the handbook for missionaries, "Preach my gospel", scripture study and prayer are listed in the chapter about commandments, to be taught to potential converts before their baptism . This normally means they will also invite people to commit themselves to have regular scripture study and prayer.
Our leaders, who we believe to be apostles of the same authority as the ancient ones, frequently tell us the same thing. This goes so far to specifically say we should make a habit of praying in the morning when we get up and in the evening before we go to bed .
In D&C 20:47, when talking about the duties of a priest, the priesthood holders are explicitely told to make sure the families pray both openly (family prayer) and in secret (personal prayer).
So, we definitely think of regular prayer and scripture study as divine commandments.
Of course the reason why we need to be told these things so often is that many struggle throughout their lives to make such habits. There are no measures the church takes against people who neglect these things. A big part of the personal spiritual life, however, certainly lives off these things.