On the one hand, it's great to have some standard methods available to all of your objects. On the other, it lessens portability (your objects now all depend on an inheritance hierarchy starting with your base bean) and it can be a temptation (if you're not careful) to create a “kitchen sink” base object where you throw in a full set of utilities for everything from validation to notifications which is not a very good way to design an app.
Personally, I use a base object to provide for language extensions that I want to have available for all of my CFC's, so I put generic getters and setters into my base bean as well as a dump() method to allow for easy CFDumping within a cfscript block. For CF8 apps I'll also drop in a standard onMissingMethod() for handling getters and setters and other missing methods.
Do you use a custom base object for your applications? If so, what do you put into it, and why?