The Book of Psalms is an example of this last category--much of the material in the Psalms are prayers addressed to God.
Psalms often are prayers based on experience, a reflection of what the psalmist has been through, and what God has done--or, in some psalms, what the psalmist wants or expects God to do next (also, of course, based on a reflection of experience--either a personal experience of the psalmist or from the shared story of a group of people).
The opening verses of Psalm 107 illustrate this type of Scripture. They call for giving thanks to the Lord for rescue. Some scholars attribute this passage to a particular point in Israel's history, the return from the exile in Babylon. The lectionary has paired it with a different point in Israel's history, the time in the wilderness. And, we can adapt them readily to our own history, of a time when we have been rescued from trouble.
Note that this particular psalm is written from the viewpoint of the nation rather than from that of an individual.
Lectio Divina: Psalm 107:1-3