Chrome: Facebook Chat is often used (if only because of Facebook's ubiquity). If you'd like to use it in its own separate messaging window, Facebook Chat Pop-Outs can help.
The extension adds a pop-out button directly to the top of all of your Facebook chats. If you didn't know that Facebook proper had left this functionality out, you'd be none the wiser. Click the button and you get a dedicated window for the chat you're talking in.