One of my most recent discoveries is Nurph. The App has received a revamp and is now more powerful than ever. It lets you invite friends into a private chat room via a simple Tweet. This is amazing if you want to take a brief connection to a new level and have a longer conversation. A great example for using Nurph is to keep your Twitter community engaged in longer talks. I also had great results using it for support purposes if you want to get feedback on your product or service.
Pro Tip: What I like best is that the App offers featured channels as well as an archive for your chat conversation.