They do actually, I was raised a Jehovah's Witness. They believe that Jesus is God's literal, only begotten son. They don't believe that Jesus and God are the same entity. So they don't believe in the holy trinity. But they definitely believe Jesus is God's son.
Generally speaking, the bits about sexual morality and the control of women are taken literally, the bits about the accumulation of wealth, the treatment of the poor and disadvantaged and social justice rather less so.
I am Catholic but wouldn't claim to be an authority on theology However my understanding is that Catholics believe that the Bible is the word of God but it isn't as simple as just picking a passage and going with the first meaning that strikes you. It's important for example to understand the context of the passage, and often there will be many layers of meaning. Plus biblical scholarship should be done in the original languages to minimise translation issues.
So that means Catholics should read the Bible alongside scholarship and tradition to make sure that they are interpreting it well.
In short, not very literal. I was taught that the creation story isn't literally true for example, but points us to a deeper truth about how the world came to be.
Biblical literalism is a fairly recent innovation, say around the last 150 - 200 years. So you won't find it in largest and oldest denominations (Catholicism, Orthodoxy). Most likely to find it within Protestant denominations, but again not everywhere. Anglicanism, which is defined as much by geography as anything else, has a wide variety of theological expressions, so one church could be very literal in their approach, the next just down the road could be very different. Evangelicals tend to have a "high view" of scripture, but this does not mean they are destined to be literalists. Sometimes those who spend a lot of time looking at the Bible are very aware of what it says and take how they read it very seriously. To quote Reinhold Niebhur (American protestant theologian) - "You can take the Bible seriously or you can take it literally, but you can't do both".
I think anyone who takes it literally has very little understanding of their own religion and how it developed.
It has always struck me as odd that these people say it's all true but then don't follow the bits they don't like such as the purity and food laws, divorce etc but will condemn people based on random verses plucked out of context.
American Baptists are very literal, but UK Baptists are more of a mixed bunch and less rigid in their thinking. I don't think that denominations have too much to do with it in this country, it is more of individual thoughts.
Biblical literalism is a feature of Protestantism so as far as I know it isn't something that the Church of Rome worries over much about.
Having said that Biblical literalism of the 'God wrote it and I believe it' variety is a minority view. Most evangelicals (subset of Protestant) hold to Biblical inerrancy which is that the Bible as we have it is what God intended. This is not the same as literalism.
The heart of Christianity is a person, Jesus and not a book.