Chrome: If you're looking to start fresh on Twitter and just want your feed to be a blank slate, Twitter Unfollow purges your entire follow list with just one click. Finally, some peace and quiet.
There are a number of reasons why you'd want to start from scratch. If you've been on Twitter for a long time, the number of people you follow has likely snowballed over the years. That gradually increasing count adds more and more noise to your feed to the point that it becomes an unwieldy deluge of information and indecipherable crosstalk.
If you follow thousands of people and media outlets, it can literally take hours to go through your list and curate who you actually want to hear from. The Twitter Unfollow extension takes a nuclear approach and simply empties your feed in just one go.
And then the rest is up to you. Personally I keep the number of people I follow below 1000 and whenever I near the ceiling I skim my list and trim the fat.