In his book The Priority of Preaching, Christopher Ash has an appendix entitled "Give God the Microphone!". In this appendix he outlines seven blessings of consecutive expository preaching. That is, preaching that takes a book (or section of a book) of the Bible and works systematically through it in a sermon series.
Christopher argues that the staple diet of feeding a congregation ought to be consecutive expository preaching. This does not mean that topical preaching (where the biblical teaching on a certain topic is taught) does not have a place. However, it ought to be the exception rather than the rule. He says: "I am not saying that we ought never to preach topical sermons; I am proposing that the normal regular week by week diet should usually be working through a book of the Bible, and this is the most nourishing basis for the diet of the sheep (ourselves included)."
He then goes on to set before us seven blessings that flow from consecutive expository preaching. Here are the seven blessings:
1) It safeguards God's agenda against being hijacked by ours
Working systematically through a book of the Bible allows us to let God set the agenda for what is heard from the pulpit week by week. It helps keep us from hijacking the teaching with human agendas, influenced by the desires for relevance, entertainment and immediacy. It gives God the microphone allows His word to set the agenda.
2) It makes it harder for us to abuse the Bible by reading it out of context
It helps us to understand the Bible in its contexts, and therefore not to abuse it by twisting it to mean something other than what God has made it mean.
3) It dilutes the selectivity of the preacher
A topical sermon is very likely to reflect the preachers framework, his partial knowledge of the Bible, his prejudices, the bees in his bonnet, and his hobby horses. Preaching consecutively through books of the Bible helps to dilute this.
4) It keeps the content of the sermon fresh and surprising
As each passage is worked through week by week the particularities of each passage shall be brought to light. Consecutive expository preaching asks "What does this passage contribute to the whole of God's revelation?" which makes for a healthy freshness.
5) It makes for variety in the style of the sermon
If we allow the style and tone of the various Bible books to shape the style and tone of our preaching then this will make for a refreshing variety in the style and tone of our sermons as we work through different books.
6) It models good nourishing Bible reading for the ordinary Christian
Topical preaching models a style of Bible reading for the ordinary Christian in which they are dipping in and out of various books of the Bible but not seeing how all the parts fit together. Consecutive expository preaching models a more nourishing style of Bible reading that is much more nourishing and sustainable, as you take a book of the Bible and read through it day by day.
7) It helps us preach the whole Christ from the whole of Scripture
It helps us to have a growing awareness of who Jesus is as the whole Bible testifies to Him, and to build up a picture shaped by the whole of Scripture, not just a few selected key passages. It helps us to proclaim as much of Christ as we can to our people, as we exopse people to as much of the Bibles rich testimony to Him.
Christopher Ash's appendix is worth reading in full, as is the whole of his book.