For me, there has always been a fine line between the prayers for the church and the world (prayers of the people, intercessory prayers, etc) and the prayer of confession. At it's best, the prayers of the people lead us from individual concerns for the local congregation out to wider concerns for the rest of the community and world. We pray for healing, for peace, for justice, for wisdom, for guidance. We recognize the places of need in the world and ask for God's intercession in those places.
The prayer of confession is our recognition of those places where we have failed to act. Through this prayer we pray for forgiveness not just for the things we have done but also for the things we have not done. We are reminded as we pray of the needy we have not helped. We are reminded as we pray of the neighbors we have not loved.
In other words, through the prayer of confession, we are reminded of the places we have failed to meet the needs of those we pray for during our prayers for others.
And if you are still reading you are probably wondering, "okay, where is he going with this?"
There is a new-ish song on the radio that I hear as a bit of intercession and a bit of confession. Every time I hear "Walk Me Home" by P!nk, I think of having a conversation with Jesus.