Psalm 103 is a beautiful song of praise. It gives us a lot of great reasons to praise the LORD. Rather than restate them in another way, I thought how what is listed here falls into several categories which give us a good example to follow. It is wonderful to pray scripture - to quote it as your prayer to God. Psalm 103 is perfect for that. But the scriptures can also be a guideline or outline for us in our prayers and public praise.
Here are the categories I saw. Do you see others?
Praise God for His benefits - all of the things that He gives us and does for us. (heals us, satisfies our desires with good things)
Praise God for who He is - His character. (compassionate, gracious, slow to anger, abounding in love)
Praise God for forgiveness of sin. (He doesn't repay us for our sins, removed our transgression from us)
Praise God because you will be joining heaven and earth in praising Him. (angels and heavenly hosts, all His works everywhere)
Praise the LORD!
Here's a beautiful worship song from a few years back that has a lot of the lyrics based on Psalm 103.