One of the most useful (and mostly free) Twitter software applications is ManageFlitter, which among other things can quickly tell you who you follow who does not follow you back, and which of your followers (and those you follow) are fake or inactive. You can then quickly take action to unfollow people within the tool and clean up your account. ManageFlitter also lets you search for people by keyword to find out who are the most followed people with that keyword in their bio, or tweets, etc, so you can strategically follow new people.
For one account I used to manage, I found the app particularly helpful to identify over 1000 people that the company followed that were totally inactive and not following back anyway. All of them got deleted. ManageFlitter limits how many people you can unfollow using the tool each day, but it is very easy to raise that number to 500+ through simple actions like writing a Tweet mentioning ManageFlitter.
If you are looking for a way to quickly filter through and unfollow Twitter users, I can definitely recommend ManageFlitter.
App Rating: B+