A post at Wm Jas Tychoneivich's blog discusses ways in which prayer may be effective. It stimulated me to add a comment about my own understanding of effective prayer - to answer that troubling question of how it is that my prayer might lead to good results that would not have happened without that prayer of mine. What is my contribution? Why is my contribution necessary?:
The way I think of this at present is that prayer is (or may be, for some people) a way of aligning ourselves with God's creative project, through love.
Therefore the difference that is made by prayer (when there is a difference - when through love we are aligned with God's purposes) is by 'Final Participation'.
That is we, as individuals, change God's creation our-selves, because (at that time, temporarily) we are fully in harmony with God's creative motivations: we personally add-to creation, from within-it.
In a nutshell; I see answered prayer as miraculous; and the miracle can be done by God alone (perhaps to confirm our faith - that worked for me!); but sometimes, by prayer, we participate in making the miracle.
Sometimes, indeed, the miracle could not have happened without our personal participation ("God could not have done it without me").
Such a view depends on my understanding that Men are destined to be (i.e God's hopes that we will become) full sub-creators, creating originally - generating from our true selves - within God's primary creation. And that it is possible for people (including, perhaps, you and me) to become aligned with God (briefly and intermittently) during our mortal lives.
If or when this happens, then prayer could lead to effects origiating from our-selves. This would be a miracle that we personally had a hand in (in the same fashion that Jesus did miracles; and for the same basic reason and by the same basic mechanism - but Jesus was in the miracle producing state all of the time, for the years of his ministry, and potentially across the full range of creation).
One familiar example is genius. The truest and purest act of a genius is to perform a miracle that originated from himself, a miracle that could not have happened without that genius's specific contribution.
Genius I take to be a model for prayer that miraculously affects reality.