The definition of conservative is generally the preservation of current hierarchies and traditions. The media has largely marched lockstep in line with the state and corporate power structure as far as I can tell. Few journalists have asked the hard questions. Even if they ask a few hard questions, they're usually safe and not at all harmful to the government.
I think the media overall could be described as swaying more to the left than the right. Organizations like CNN try to stay in the middle, but they often show a little liberal bias at times. MSNBC on the other hand has chosen to go fully left, in reaction to the success of Fox News' complete domination of the conservative market.
Media is so broad. Television, radio, internet, music, and the rest. If you add the sum of all parts, I think it would learn liberal. Maybe that's bias as I am, myself, liberal. There are certainly a wealth of conservative media to be found. And if you count Churches as conservative media, then that may tip the scale in their favor, but I do not count that as a source of institutionalized media. Or at least not the intentional type.
I think that it depends a lot on what publication/news source you are dealing with, but for the most part, the media is liberal. I'm particularly thinking of the three major networks (ABC, NBC, CBS), and it seems like all of their news is presented in a somewhat liberal fashion. However, when you start talking about cable news, the opposite can be said of Fox News.