1. Happier Users
With plugins, users are not limited to the functionality built into the base product. They can enhance the product/customize it to their needs by installing third-party plugins. This is the obvious reason. In fact, many people think this is the only reason.
2. Happier Developers(!)
Plugin-based programs are usually very easy to debug. Let me tell you how a typical debugging cycle works in such programs: You start (as always) by writing a test that captures the bug. Then you gradually remove plugins from the program until you arrive at the minimal program that still produces the bug. If you do it via a binary-search (over the set of plugins) the process will converges quite quickly.
Usually, you end up with a very short list of plugins. A few educated guesses will help you spot the bad plugin right away. Even if you're out of guesses, you're still in a very good position: the amount of code that needs to be scanned has been dramatically reduced.
Compare that to a program that is not plugin based. Such a program cannot function without any of its parts. Thus, you have no systematic way to reduce the amount of code involved with a bug.
3. Plugins are Agile
Breaking up a user request (story or even theme/epic) into tasks is usually a breeze in a plugin-based program. One should simply break the story functionality-wise and implement each piece as a separate plugin. This is much easier than breaking a story according to implementation-oriented tasks. Bottom line: less overhead due to iteration planning.
4. Easy Collaboration
A real story: A few months ago my team was asked to assist another team with their product. That product had plugin support so we simply implemented our additions as plugins. We were not afraid to break things because we had no access to the source code of the core (big plus). Also, the core was written in C++ but the plugin system is in Java (second big plus).
That's my top four reasons. As you can see only the first point is user-oriented. The other three points are all developer-oriented. Surprising, isn't it?