I think I managed to find what I was looking for.
After doing some research in here, on stackapps.com, I have finally found what I was looking for, namely an easy way to get notified about new answers, posts and/or comments for the topics that I am interested in, topics listed on all sites from StackExchange network.
The application is called StackTracker (a Cross-platform desktop notification app) and it has support for Windows and Mac OS X. I am not sure about Linux, I tried to find a link for the Linux version but I seem to be getting nowhere. So, I just use StackTracker in Linux via Wine software.
