Philippe DeCroy of the Volokh Conspiracy talks a bit about the editorial effects of the Harold Raines regime on the New York Times. Not being a regular NYT reader these days (I did read it for about a year in college, but decided it wasn't worth spending the money on later in life), I can't vouch for Philippe's impression of a decided turn toward the paper's wearing its liberalism on its sleeve; Philippe argues this has caused him(?) to lose confidence in the paper's reporting.
The "problem" of media bias has been widely studied in political science and communications studies. At least in the modern U.S., most media bias has been seen primarily in terms of the framing and agenda-setting powers of the media: deciding how issues are to be presented and what issues should be discussed. Perhaps the most thorough work on this has been John Zaller's The Nature and Origins of Mass Opinion and his work on the impacts of the media on public opinion (most notably, "The Myth of Massive Media Impact Revived"). One of Zaller's arguments is that people gain political knowledge due to the information that they are exposed to; this information can be either factual (as we traditionally view "information") or biased in some way. For people to make "good" or well-informed political decisions, they have to be exposed to multiple sources of information, and they have to be able to sort out that information. Other studies have shown that so-called "negative advertising" is a very good source of this information in political campaigns, because unlike most "positive" advertising, it talks about issues and other things that are politically relevant. Despite the ravings of the campaign finance reform crowd, who want strict limits on political advertising, negative TV campaigns tell us much more about candidates than anything else.
Similarly, the media provide information. The best way to learn (i.e. get information) about something is to find lots of reports of the same event from different perspectives; Google News is a near-perfect implementation of this capability, although you'll probably find that most of the reports are based on one "unbiased" AP report, which limits one's ability to integrate: to take the event viewed from various perspectives, process them through the observers' biases, and come up with what actually happened. Somewhere between The New York Times's version of events and that presented in The Washington Times is the truth; if you're open-minded enough to read both, their individual biases don't matter so much as your ability to recognize those biases and include them in how you evaluate what happened.