The idea of a package management system is probably one of the best since sliced bread or a GUI. It's amazing! To install something you don't even need to go onto a site to get something, you just pop open the program, search for it in the list and install it. Simple! It even handles updates for you.
I remember the days of Fedora Core 1 when they had the simple package manager. It was great, every time I tried to run it, it would crash the system. Really useful. Using yum wasn't so bad, except when yum would think you had a package installed but the other packages you were trying to install didn't agree. I was still a Linux newbie back then, there was probably a quick fix to it but of course, to a new user, it's easier to reinstall Windows. When problems comes up in Linux, the solutions should be less effort than installing Windows, otherwise people won't stick with the system for very long.
Of course, you're dependent on the package being in the repository. If the repository was small, this would be a problem, but Ubuntu's repository is gigantic (a quick glance shows 22841 with the Wine repository added). They're also adding packages all the time.
It's great for developers, for example if you want to use a particular library (ie. Glade) you can easily get it and use it. Then when you distribute the program, you can also have the other people install the libraries you need no problem. The only downside is that Windows has yet to reach the package-managed universe, so you have to figure out how to get these libraries to work on Windows.