The mass media does have a Leftward tilt; not as far Left as the Right makes it out to be (and slanting it the same amount Rightward would be no fix!), but it is there.
Comparisions between general-population polls and media-only polls have shown this misalignment.
Here's one report:
http://secure.mediaresearch.org/news/MediaBiasBasics.html I am not entirely pleased with their graphics, which could be more clear. One of the better gun bloggers did a more concise and clear illustration, but I have not been able to find it.
There are things that keep this from being as dire as it might look:
First, all of the studies and most of the outcry concern old media. Conventional news media isn't just old, it's going away. Increasingly irrelevant, it's like the last of the steam locomotives in commercial freight service: large, impressive, emblematic, but no longer vital.
While "the media" is a nice concept, even traditional media is not really monolithic. The various outlets are run and owned by differing people and groups. The good thing (IMO) about Fox News is that it's pulling in the other direction and getting good ratings at it. Me, I vote Klingon, so every so often I think the newsies on Fox are plain nuts, as off-base as NBC or CNN but in the other direction; doesn't matter. The overall trend is what matters.
Print media, cry all you like but the dead-tree version is dead. Profits are shinking like ice on a summer sidewalk: what's in the paper, how it leans, really doesn't matter any more. Grandad reads the paper, Dad might look at it and I bet you rarely do more than glance. If it's not on the front page in screaming type, maybe on the Editorial page, with the comics or in the Sports section, it's not there. News magazine audiences are tiny, fragmented. It's doctors-office fodder -- even there, sports mags, women's mags and National Geographic (et al.) are crowding them out.
Films: read history. Actors and theatrical troupes have always been "out there," the bane of All Right-Thinking Villagers. What we have now? More of the same. Ignore them, rail against them, doesn't matter. They'll get up on stage and make faces all the same; they have to. You can steer what stories they present and how they tell them by what you spend your money on -- and keep those gun-grabbin' actors looking the hyprocrites they are making fine action-adventure films.
Two kinds of new media do matter: online decentralized news from blogs and BBSs and any oddball or old-media enterprise with a website soapbox (a lot of this is by specific request or in response to webseaches), and "pushed" news that comes to your homepage, celphone, PDA, etc. by subscription of some sort. Even the second sort has a greater element of pick and choose than any old-media mode,
and provides greater feedback to the supplier.
The thing to remember is that a whole society, a free society, is well-nigh impossible to steer and ours is starting to push back against its would-be helmsmen more and more. "The Media" is moving to the center and will continue to do so, not because there's any upsurge of goodness or morality (the Left, while encompassing plenty of eejits -- and is the Right altogether free of them? -- doesn't lack for good and decent people, though some of them have mighty odd notions) but because
it wants our money. The only way it'll get us to buy is by offering us what we want.
Being selective is a good idea. A blanket boycott? Not for me. I live in a highly-connected world; I'm keeping my 500-channel satellite TV, and it's keeping track of what I watch. If you won't tell 'em what they want, they won't know to sell it to you.