One useful tool I've recently discovered is Twunfollow.com, which gives a daily digest of Twitter accounts that have unfollowed your account. This visibility is particularly useful in that it provides an extra level of insight- an indication of how your audience reacts to certain themes of tweets, as well as enabling the option to unfollow users back.

On the flip side, I have used Vizify's Tweetsheet in the past to gauge what my MOST popular tweets are. Tweetsheet measures tweets that have been retweeted most and by whom, which is an obvious illustration of which style/theme of tweets appeal most to your community. I'm still searching for the ideal Twitter engagement indicator, however, as Tweetsheet does not track mentions, only retweets. Suggestions welcome!