From the comments

[wolk-off.livejournal.com]

For those who miss the genuine sound of real Russian speech :), there are radio stations streaming over the Web. Try Эхо Москвы since it's more a news/talk station, so they speak there a lot: live; news-on-demand. The later is more useful because it's news which you can read along with the listening.

In live section, there are streams for Winamp and for Windows Media Player. Latest news section has only a Winamp stream.
They also claimed that it was playable by Real Player, but I haven't tested it.