An ambitious task, to be sure.
Design is not always my strongest suit, but experimentation and practice are key to getting better. With that end in mind, I’ve taken the currently fairly dull Apple iTunes logo and changed it completely.
iTunes already has an incredibly diverse user base, but the largest section of it is made up of youth ages 12-17, with a slight male bias, according to Nielsen NetRatings. This particular group is unlikely to respond to a logo change at all, so a logo redesign should be done with attracting another portion of the market as the main objective.
There should be a more dynamic, interesting, modern look and feel to the new logo, eliminating what appears to be old-fashioned or outdated about it. The blue in the current logo can likely be kept, as it appeals to the widest audience, but other design elements should be used or modified to create an energetic, professionally youthful appearance.