A prayer that God would come and do something here and now, in the gathered church. For example, at the beginning of the service, we ask God to come and be with us as we draw near to him; at the preaching of the word, we ask him to speak; at the beginning of Holy Communion, we ask him to feed us on Christ. The invocation is solemn and humble (God is not at our beck and call!), but bold (because it responds to and claims God's own promise).
Praise and Adoration
Technically distinguishable, in worship the one must flow into the other. Praise is the acknowledgement before God of his glorious nature and character; adoration is the lifting of our hearts to bask in the same. Here we take our eyes completely off our own needs and situations and focus on God in prayer.
As sinners in the presence of a holy God, and as beneficiaries of gospel forgiveness, we confess to God that we have sinned against him. The Christian confession of sin is not a grovelling, but a humble acknowledgement in God's presence that we have failed and need both his forgiveness and his help to change. The prayer of confession is traditionally sandwiched between biddings, which explain God's delight in forgiving confessed sin and invite us to come, and words of assurance, which remind us that confessed sin truly is taken away through the gospel.
Focusing on particular things that we have received from God, we give him thanks. This could be for particular answers to prayer, or for gospel blessings received through Christ. In a sense, this a prayer of praise and adoration that particularly views God's character and nature as it has affected us.
This means both the church as a whole interceding with God for its own members who are in particular need - for example, the sick - and also the church interceding for those outside its particular membership. The church prays together for the church worldwide, and for the world outside the church. This is a key part of what it means to be a kingdom of priests.
A short prayer of praise which might be appended at various parts of the service - for example, the Gloria Patri.
Only implicitly a prayer. The speaker pronounces a blessing over God's people, and in that way stands in the place of God; but of course, they can't really stand in the place of God (they cannot of themselves make the blessing anything more than a pious wish), and so the implicit prayer is that God would make the blessing effective. If we are pronouncing gospel blessings, though, we do know that they are in accordance with God's will for his people, and so they can be pronounced with authority.
1. Have I missed any?
2. How do we ensure that the richness of Christian prayer is reflected in our worship services?