ThinkUp is a free, open-source web application which can archive your Twitter, Facebook and Google+ activities and help you to review them later.
At its simplest this may simply mean allowing you to search all your tweets to locate one from long ago.
You can also produce graphs of various information, though, such as charting how your followers have increased over time. There's an option to geocode replies and view them on an interactive map. And you can even publish and embed conversations on your own website.
Please note, though, this is a web application, not a desktop app, so you'll need to deploy and run this on your own server. This doesn't have to be complicated - the ThinkUp Launcher can do it in just a few moments, and free of charge for a year if you're new to Amazon EC2 - but if you're new to web apps then it may still require some effort to understand how everything works.