Sovereign Grace Music has produced some great CDs, and now they have released a new one on the Psalms. You can hear some samples of each Psalm here, and they also provide a free download of "Praise the Lord" (their version of Psalm 150). Be sure to download the lyrics too. If you are familiar with singing the Psalms, this is not quite the same. But if you have not been introduced to Psalm singing, you can start now.
Speaking of Psalm singing, at my church we started learning a new Psalm each month early into my ministry, and this "Psalm of the Month" plan has been very encouraging to our whole church. We started by learning some popular Psalms, such as Psalm 23 to the tune of Crimond. We also learned Psalms to tunes we already knew (such as the tune to "Amazing Grace," or Psalm 100 to the "Doxology"). If you are interested, you should purchase a good CD like the Psalms of Scotland by the Scottish Philharmonic Singers. There are a few places on the internet that have text and tunes, but the tunes are midi files (such as here and here and here). The truth is that nothing can replace the experience of singing the Psalms in worship with the people of God. I would have to say that learning to sing the Psalms has been one of the greatest spiritual benefits for my life.