My kids have a fine appreciation of Paul Simon (and Garfunkel) from their times as babies. I preferred Me and Juilio......and Loves Me Like A Rock, dh preferred The Boxer. We weren't traditional lullaby type parents, we just sang the songs we liked. Sometimes dh would even break out the guitar (accoustic).
I used to sing my son the Aggie War Hymn from Texas A&M University when he was a baby.
I sing LSU’s Hey Fightin’ Tigers to my son among other things.