I must admit that I'm not listening to a great deal of music myself at the moment, but I don't think it's altogether wrong to listen to music. After all, God created music, and there are NUMEROUS references to singing and instruments in the Bible. To cite just one:
I will sing a new song unto thee, O God: upon a psaltery and an instrument of ten strings will I sing praises unto thee. (Psalm 144:9)
God is certainly pleased with the right kind of music:
And it came to pass, when the priests were come out of the holy place: (for all the priests that were present were sanctified, and did not then wait by course: Also the Levites which were the singers, all of them of Asaph, of Heman, of Jeduthun, with their sons and their brethren, being arrayed in white linen, having cymbals and psalteries and harps, stood at the east end of the altar, and with them an hundred and twenty priests sounding with trumpets:) It came even to pass, as the trumpeters and singers were as one, to make one sound to be heard in praising and thanking the LORD; and when they lifted up their voice with the trumpets and cymbals and instruments of musick, and praised the LORD, saying, For he is good; for his mercy endureth for ever: that then the house was filled with a cloud, even the house of the LORD; So that the priests could not stand to minister by reason of the cloud: for the glory of the LORD had filled the house of God. (2 Chronicles 5:11-14)
Evil spirits hate godly music:
And it came to pass, when the evil spirit from God was upon Saul, that David took an harp, and played with his hand: so Saul was refreshed, and was well, and the evil spirit departed from him. (1 Samuel 16:23)
So when used aright, music can be a wonderful thing indeed. Unfortunately, Satan has greatly corrupted music, and there is a reason why he is so good at it. Before he fell, he was a remarkably beautiful creature and highly adept in music:
Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle, and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created. (Ezekiel 28:13)
So it is certainly a challenge nowadays to find truly godly music that has not been tainted in some way by the Devil. CCM is certainly corrupted, based as it is on a foundation of rock and roll. And as you say, some of the old hymns can be tainted by bad theology (at least they don't have a rock beat, although that said, some have been "jazzed up").
I like some of the hymns of Fanny Crosby. Fairly sure that Blessed Assurance and To God Be the Glory are sound. They have nice happy melodies too (Crosby was a Methodist, and they're fans of joyful singing, although they have a few theological issues). The classic oratorio, Handel's Messiah, is based on the King James Bible. (If anyone knows of issues with Handel's Messiah though, please advise.) I used to quite like Majesty Music, which do have some quite sound and godly tunes. However, I have gone off them a bit now as they celebrate Christmas (i.e. they put out material with Christmas songs) and some of their Patch the Pirate material for children (which I've never actually listened to) has apparently started to take on contemporary flavours. If you like bluegrass-type music, I have enjoyed some material by the Marksmen Quartet and Seminole String Band, although I wouldn't give either a 100% endorsement (for instance, the Seminole String Band includes a couple of songs by contemporary composers Keith and Kristin Getty in their repertoire). But I have found some of their stuff to be edifying.
Not sure if I've actually helped you much there. It's no easy matter to find real godly music that is "unspotted by the world". But certainly, if you can find some, there is absolutely nothing wrong with listening to it!
