One of the funky things Google does is let you display your current music tract as part of your status in Google Talk. Google aggregates this data to produce Google Music Trends. If they had launched that feature last month then there would have been a privacy blog post about it.
This "music history" is also stored as part of your Google Web History. It's nice to be reminded of what you where listening too (though a shame it doesn't work with the likes of Last.fm) but a song isn't a web page and Google's Web History isn't very good at coping.
For example, you can try and mark a song as a favourite/bookmark it and two things will happen; 1) all the songs in your history list will be bookmarked and then 2) Google won't remember and will reset the bookmark star back to blank.
While you have songs marked as a bookmark, though, you can start to get really silly. Try changing the name of a song.
However, when you try and save your edit the Google bookmark system does't cope. It throws bad request errors back at you.
Just imagine a Google Music system which let you associate favourite tracks with certain web pages - when you browse onto the page you could have the option of the associated track playing. If that sounds crazy then remember there are iGoogle Gadgets which let you control iTunes. What about a Google Talk that let you associate music with Contacts? You could have a 3 second clip played in response to a talk request or even have an entire track played in the background when you begin a conversation. Heh. That would either drive you insane or drive up your electronic music collection.