As mentioned in other answers, the ability to add implementation to an interface was added in order to provide backward compatibility in the Collections framework. I would argue that providing backward compatibility is potentially the only good reason for adding implementation to an interface.
Otherwise, if you add implementation to an interface, you are breaking the fundamental law for why interfaces were added in the first place. Java is a single inheritance language, unlike C++ which allows for multiple inheritance. Interfaces provide the typing benefits that come with a language that supports multiple inheritance without introducing the problems that come with multiple inheritance.
More specifically, Java only allows single inheritance of an implementation, but it does allow multiple inheritance of interfaces. For example, the following is valid Java code:
class MyObject extends String implements Runnable, Comparable { ... }
MyObject
inherits only one implementation, but it inherits three contracts.
Java passed on multiple inheritance of implementation because multiple inheritance of implementation comes with a host of thorny problems, which are outside the scope of this answer. Interfaces were added to allow multiple inheritance of contracts (aka interfaces) without the problems of multiple inheritance of implementation.
To support my point, here is a quote from Ken Arnold and James Gosling from the book The Java Programming Language, 4th edition:
Single inheritance precludes some useful and correct designs. The
problems of multiple inheritance arise from multiple inheritance of
implementation, but in many cases multiple inheritance is used to
inherit a number of abstract contracts and perhaps one concrete
implementation. Providing a means to inherit an abstract contract
without inheriting an implementation allows the typing benefits of
multiple inheritance without the problems of multiple implementation
inheritance. The inheritance of an abstract contract is termed
interface inheritance. The Java programming language supports interface inheritance by allowing you to declare an interface
type