When I was a little kid, I loved music, but it was, as you said, just pretty noise, and I sang along just mimicking the sounds. It wasn't until an adult told me that I was just making noise and not singing the song correctly that I realized it was supposed to be words. At that point, I became fascinated with it and wrote down the lyrics to every song I had on pieces of construction paper. But doing so, I misheard a lot of them. After I'd read over them a few times, I realized that they weren't just random words, that they were actually saying things. This was a huge revelation! At that point, I could listen to the songs again (over and over and over) and compare them to what I'd written, and figure out what the actual lyrics were, judging by what made sense in context. I can't tell you how many hours I spent doing this when I was little. I guess it was an obsession, but I'd forgotten about it until your thread reminded me.
Anyway, I'm sure I've experienced what you're talking about, but I can't think of any specific examples. Well, except for one. It was the lyric "Life will never be the same again." I actually remember crying as I listened to that because I suddenly realized the truth of it.
This is kind of interesting to me now, since one of my favorite singers is Azam Ali, and she is known for singing without using any actual language. It's all just sounds... like how I sang before I realized they were words.
[youtube]http://www.youtube.com/watch?v=9fxrLIZpuvo[/youtube]