Today is the feast of St Michael and All Angels. Angels are funny things. They are all over the place in Christian architecture and iconography, and for those in more liturgical traditions they form, in theory at least, part of the context of worship ('with angels and archangels...'). But I am not sure we have much practical use for them. Indeed, they are something of an embarrassment. It is just possible to construe worship of God as being compatible with our modern world; after all, God can be re-envisioned fairly easily in ways that fit the post-enlightenment paradigm in which we live. But to believe in Angels puts you in the same realm as people who believe in the healing power of crystals, and people who take astrology seriously, and whoever it is who reads all those books about near-death experiences.
It's impossible to avoid the fact that one cannot tell the Bible story without angels. The presence of Gabriel at the Annunciation is sufficient to secure their place in the narrative. But other than these 'big events' - with which I suspect we are happy because of long exposure and also the sense that these are dramatic one-offs and therefore not normative - angels mostly appear within those parts of Scripture for which we have least time. The weird bits of the book of Daniel give a portrait of angelic warfare, linked to human prayer, which seems uncomfortably mythological. The various scenes in Revelation featuring angels are often so bizarre as to require explaining (away) in other terms.
All in all, I think for most of us angels are acceptable backdrop, so long as we don't seriously have to believe in them or their activity.
I think we could gain a lot by recovering a genuine, practical faith in the work of angels. For starters, a God who intervenes by the ministry of angels is very clearly not the god of the deists, and so a principal idol is cast down. Moreover, the presence of angels around us signals God's own presence in the mundane details of our lives.
Perhaps the biggest thing for me is that to believe in angels as the Bible portrays them is to believe that we are caught up in a world of spiritual activity - and more specifically spiritual conflict. The Archangel Michael cast down the dragon, who now roams the earth in fury.