The image that comes to mind for many of us when we think of filibusters is Jimmy Stewart's filibuster in the movie, Mr. Smith Goes to Washington. This is the image of the lone senator, rising to his feet to protest a piece of legislation that he finds morally bankrupt, and not sitting back down until he has literally talked the bill to death:
This image probably holds even for those of us who haven't seen the movie, so influential and compelling Stewart's performance has been, which is why so many Americans (and US Senators) are loath to get rid of it.
There's a problem with this image, however. It isn't how it is done any more. Now to filibuster, Senators don't have to walk out on the floor of the Senate, they don't have to talk all night, they don't even have to talk at all! All they have to do is pick up a phone. Or better yet, they can have one of their staff pick up a phone. Thus, it's not surprising, that filibustering is much more common than it used to be as the graphic below illustrates:
There have been attempts to make filibustering more difficult, back to the way it used to be, but most of these attempts are, well, filibustered. They are typically put forward by the party in the majority and fought by the party in the minority. Thus, currently you find a number of Democrat Senators supporting limits to the filibuster when just a few years ago (when they were in the minority) they opposed it. Similarly, Republicans, who are in the minority, oppose such limits, but just a few years ago, they supported them.
Back in December NPR's Planet Money produced a interesting podcast on the filibuster ("Schoolhouse Rock Was a Lie: Or, How The Filibuster Ate Washington"). You can listen to it at the Planet Money website or download it from iTunes.