I read Twitter almost exclusively via my custom personal news reader that I developed like 5 years ago. It allows me to do a variety of things to increase the signal/noise ratio of tweets. For example, it aggregates tweets by person in chronological order [1] - making the daily aggregate of a person's tweets into a single post akin to David Winer's original blog. What I also did is stop following non-humans except for rare instances. Both helped me cut through the noise by quite a lot.
Then recently, I excluded all retweets. It's quite amazing how little actual new thoughts and opinions are shared on Twitter - getting rid of retweets cut out easily 80% of the tweets I'd see. And I'm OK with that - I think too many people retweet reflexively, without real thought and it ends up being a waste of time.