http://builtwith.com as John mentioned earlier is your first step, and as others mentioned if you are just beginning go with WordPress, about a third of all new sites now are on WordPress so you have the support, security and flexibility that goes with that.

If you're looking at a WordPress site you like the features of, you can dig a little deeper with http://www.wpthemedetector.com/ to see the theme they use and often the plugins they use. In my experience it only recognizes about 30% of the plugins out there, but often you'll get some great insights into how a site has been put together, and Viktor's tips above will help you find even more.