Get a good app
Using the Twitter.com site or the Twitter iOS app is one way to keep up with Twitter from your Mac or iPhone, but it's certainly not the only way. You can choose from many different apps to track your tweets. Some Twitter client developers focus on polishing their list experience, as well as a host of other useful perks beyond Twitter's Website and official clients. (Twitter for iPhone, for instance, doesn't even let you add to or manage your lists.)
On the iPhone, look at Tapbots' $3 Tweetbot (my personal favorite since it debuted in April last year), Stone Design Corp's $3 Twittelator Neue, and Twitter's other free client for Mac and iOS power users, called TweetDeck.
On the iPad, Tapbots' $3 Tweetbot for iPad offers a strong choice with easy access to lists and other tweet management tools. DW:design's $4 Tweetings and Naan Studio's $5 (free with advertisements) Echofon are also decent options for managing and reading your Twitter lists.
Good list experiences are a little slimmer on the Mac. Take a look at Naan Studio's $5 (free with advertisements) Echofon and YoruFukurou Team's free YoruFukurou.
Give overly chatty accounts (or topics) a timeout
Let's say you like the current flock of Twitter accounts you follow, but every now and then a handful of them get chatty. Maybe they liveblog dropping their kids off at daycare too often or they can't resist jumping in on every hashtag that rises up Twitter's trending list. Whatever the reason, some Twitter clients offer the option to mute things like users, hashtags, or even clients. This is useful when you don't want to see any posts from anyone about, say, football or Foursquare, as well as for uniformly giving Instagram photos the boot.
Now, I should note that Twitter does not yet officially support any kind of "mute" feature, much to the annoyance of many of its users. But some apps offer the feature anyway, including: Echofon for iPhone and iPad, as well as Echofon for Mac; Hibari; Tweetbot, both iPhone and iPad versions; Tweetings; and Twittelator Pro for iPhone.
Generally, mute options are offered in increments of time such as a day, a week, a month, or forever. So yes: if you really need to, you can give in to that one really persistent friend begging for a follow, but never have to actually see his or her tweets--as long as you use an app that supports the mute feature.
Search instead of follow
Who says you have to follow anyone at all? Plenty of people use Twitter as nothing but a research tool in addition to, or in lieu of, their personal aspirations for tweetness. Terrible lingual puns aside, one of Twitter's other useful management tools is "Saved Searches." These let you see what everyone across all of Twitter is saying about a particular keyword.
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