Before you shout, "Yes, of course, He did!" you may want to take a look at this particular psalm. Here is the text of the psalm as found in the New Living Translation of the Bible:
"Beside the rivers of Babylon, we sat and wept as we thought of Jerusalem. We put away our harps, hanging them on the branches of poplar trees. For our captors demanded a song from us. Our tormentors insisted on a joyful hymn: 'Sing us one of those songs of Jerusalem!' But how can we sing the songs of the Lord while in a pagan land? If I forget you, O Jerusalem, let my right hand forget how to play the harp. May my tongue stick to the roof of my mouth if I fail to remember you, if I don't make Jerusalem my greatest joy. O Lord, remember what the Edomites did on the day the armies of Babylon captured Jerusalem. 'Destroy it!' they yelled. 'Level it to the ground!' O Babylon, you will be destroyed. Happy is the one who pays you back for what you have done to us. Happy is the one who takes your babies and smashes them against the rocks!" (Psalm 137)
First, it is obvious that this psalm was written from the perspective of one of the Jewish exiles in Babylon. It is also clear that this individual was part of a group of temple musicians, and that they were missing their home in Jerusalem. Thus it is certainly understandable that these folks did not want to perform the Lord's songs (hymns) for their pagan captors.
However, their longing for Jerusalem is portrayed in the psalm as obsessive. After all, it is Jerusalem that this writer was focused on - not the Lord. Is it ever appropriate to make any physical thing or place one's "greatest joy." God is appealed to only in the context of settling the score with the people who have wronged them (the Edomites and the Babylonians). The pain and bitterness over what has happened to them is made clear in every line.
Finally, the author rejoices at the prospect that Babylon will one day suffer a similar fate - that they will be repaid for what they did to the Jews. He/she even goes so far as to say that the one who exacts the retribution will enjoy taking the Babylonian babies and dashing their brains out against the rocks. Can you imagine any crime that would justify taking an innocent baby and slinging it against some rocks? How is that fair, righteous or just in any universe?
Could it be a mistranslation of the text? The King James Version of the Bible renders this passage as: "Happy, shall he be, that taketh and dasheth thy little ones against the stones." (verse 9) The New International Version renders the same verse as: "he who seizes your infants and dashes them against the rocks." Strong's Exhaustive Concordance of the Bible informs us that the Hebrew word translated as babies, little ones and infants appears thirteen times in the KJV as "children," three times as "infant," two times as "babes," and one time each as "child" or "little ones." Likewise, the Hebrew word translated as smashes, dasheth and dashes appears nine times as "break in pieces," three times as "break," three times as "scatter," two times as "dash," and one time as "dash in pieces" (and in similar contexts in a few other places). So it sounds like the translators got it right.
Does this kind of cruel, heartless and vindictive behavior sound like anything that Almighty God would ever engage in or condone? I don't think so. Do we really want to attribute this passage to the inspiration of the Lord? What do you think?