Perhaps the most obvious use is laziness - why bother maintaining X methods across Y classes, when you can just have your subclasses inherit from your main class and maintain the non-overriden methods there . . .

Eek! Such is really false-laziness, as it tends to break object relationships into whatever the programmer felt like at the time, instad of a logical flow. It tends to make things a lot harder over time, since two classes that really have nothing to do with each other are suddenly in a parent-child relationship, just because there was a bit of code in the parent that was also needed in the child.

Down that path lies many a broken OO project.