Start with your RSS reader
Google Reader is my go-to RSS reader, and I use it to monitor selected Twitter posts, as well as feedback and engagement on my Facebook pages. I subscribe to the full Twitter feeds of a few individuals--the ones for whom I never want to miss a post. Just enter the URL for their Twitter accounts where you add subscriptions, and you'll see the posts right in your RSS stream. I also subscribe to my own tweets, which helps me monitor whether they posted and also gives me an archive. To monitor Facebook page engagement, click on "Notifications" on your page, then "See All Notifications," and click on the "Get notifications via: RSS" link. Then enter that URL into your RSS reader to subscribe. Now, when someone likes, comments or shares my Facebook page posts, I don't need to leave my reader to find out. For free.
Make full use of Tweetdeck and Favstar
I've loved Tweetdeck from the get-go. It's now owned by Twitter, but still retains my favorite feature: You can add accounts for Facebook individual accounts or pages, Foursquare, Twitter, LinkedIn, MySpace and Google Buzz. You also can add columns for each of those accounts, and post to them accounts without leaving Tweetdeck. Set up search columns in Tweetdeck to monitor specific keywords, hashtags, or your own posts. Use Favstar.fm to track who's favoriting and retweeting your tweets; you can also set up an RSS feed so Favstar notifications come to your Google (or other) Reader.
Stay alert to new, free tools
Sometimes, all you want to do is monitor your own Twitter feed, especially when you want to retrieve an ancient tweet that's needed now. That used to involve endless scrolling through your tweets on Twitter, or, if you set up a feed in Google Reader for your own tweets, a search there. Now the CloudMagic browser extension for Chrome or Firefox takes searching your Twitter feed up a notch and makes it even easier--I've been using it all day and wondering where this has been all my life. Try this. You won't regret it. And if your geographic reach is important on Twitter, take a look at TweepsMap will show you your Twitter followers by country, state or city, in map or list form.
Want to save all these free records? Follow the tips in this post on using ifttt, Evernote and other tools to create a content stash.