Start up a command prompt and type netstat -n or whatever flag you want. You'll basically get the same information. Microsoft also offers a little tool called PortReporter (too lazy to find the link) that has more detailed information. That in a way answers some of your questions.

As to what connections should you trust, trust what you want. If you know you have AIM running then expect port 5190 to have something using it, if you're using irc, expect port 6667 or whatever port you're using open. People might gawk and talk crap about viruses and backdoors, which I know happen, but if you trust your browsing habits and downloads, then I don't think you have anything to worry about.