At the time of writing I follow about 50 people and those 50 people generate about 300-400 tweets a day. The number of tweets passing before your eyes if you follow hundreds of people is going to be overwhelming.
The obvious solution to tweet-overload is to stop following people, but you probably followed them for a reason and perhaps that reason was a handful of really interesting tweets a day, or maybe you were just stalking a celebrity.
You can help filter the noise with a desktop client such as Tweetdeck. Unfortunately, such Abobe Air based applications don’t work for me as I use a number of different computers each week, with varying specifications, and some of them I have no control over what is installed.
I only follow people who tweet tweets that, to a to a large degree, are interesting to me within my area of work. I then use a combination of Netvibes, the Twitter Search widget and the Tweetgrid Widget (for hashtag searches) to follow people, topics and keywords that I don’t want in my main twitter-stream. I have then collected all of these together on a “twitter” tab in my Netvibes. This tab has become, in effect, a Tweetdeck for me. An example is available here for you to view and copy.