I have some application settings that I'd like to add to my configuration file, but I'd like to group them outside of the normal "appSettings" section. My thought was that I would just create another "section" element within the "configSections" node of the config file, setting the "type" equal to "System.Configuration.AppSettingsSection, System.Configuration, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a" and the name to "MyCustomSection". I'd like to not re-invent the wheel, as I'm just looking to use the standard appSetting <add key="some key" value="some value"> node structure within a different section name. I'm basically looking for some opinions as to why I wouldn't want to reuse the AppSettingsSection class.
Forget it, I just found the correct alternative solution for my issue: http://blogs.msdn.com/kaevans/archive/2004/08/19/217177.aspx
You may eventually find that this approach is quite limiting as all you are going to get are key value pairs. You should consider taking this one step further and implement your own configuration section. It is very easy to do and gives you the flexibility you will need later on.
The first thing you will benefit from is you are not restricted to string values, you can get integer, boolean, guid and string values out of your configuration object without any work and anything else you need you can create custom type converters.
A good starting point would be: Unravelling the Mysteries of .NET 2.0 Configuration
If you do follow your current approach you will find that you will need to refactor further down the road.
If you want to take it to the next level and be configuration ignorant and not be dependent on a particular configuration implementation you can look at my blog post on configuration ignorance.
Furthering Bronumski's answer, there is actually a designer for custom configuration sections that saves you a lot of typing: