Those constructors usually are protected and never public. Actually, that's something that the FxCop tool (www.gotdotnet.com/team/fxcop/) will enforce in your assemblies - if you are not using that tool, you should consider it right away. It enforces best practices across your code.
So, the constructor serves the purpose of initializing whatever is needed on the base abstract class, whenever a descendant class is created. Note that if the abstract class offers only a single version of the constructor – say, receiving a parameter, or not receiving a parameter – it HAS to be called by the descendant class. In the case of a 'parameterless' constructor, this happens automatically whenever the derived class is constructed.
This was first published in April 2005