The privacy statment (this one is for WMP 10) does a pretty good job of listing all the ways it might phone home (or phone somewhere). Many of them can be disabled, some it will ask about during install as well. It doesn't leave any background processes running that I am aware of.

[link|http://www.microsoft.com/windows/windowsmedia/mp10/privacy.aspx|http://www.microsoft...mp10/privacy.aspx]

As a media player I like it. I sometimes wish I could launch two instances of it (one for music, other for muted video), but that doesn't come up much.