It's too bad Grooveshark probably won't be around long enough to see this webapp improve, what with every single major record company suing them for all they are worth at the same time.
Luna is the name of that wallpaper, it came with Windows XP. But there are several variations of the theme in the thread with more space-oriented pictures.
Cyanogenmod bakes an equalizer right into the phone's os.
Up until that point I used astro player beta, for its equalizer, then jumped over to Mixzing when it got one.
But now I use the default music player, which has been greatly improved in cyanogenmod, bakesin FLAC and APE support, adds lockscreen support, and has the ability to skip songs with a long press of the volume buttons so it doesn't leave my pocket.
@TheNimboo: Careful there, this information is quite outdated.
I would check various forums for more updated rooting information if I were you.
As for my list, most of those apps have been replaced or incoporated into other apps. I'll make a new post with my current favorite apps sometime soon.