I will choose Java as an example, most people know it, though every other OO language was working as well.
Java, like many other languages, has interface inheritance
It's funny to answer my own question, but here's something I found that is pretty interesting: Sather.
It's a programming language with no implementation inheritance at all! It knows interfaces (called abstract classes with no implementation or encapsulated data), and interfaces can inherit of each other (actually they even support multiple inheritance!), but a class can only implement interfaces (abstract classes, as many as it likes), it can't inherit from another class. It can however "include" another class. This is rather a delegate concept. Included classes must be instantiated in the constructor of your class and are destroyed when your class is destroyed. Unless you overwrite the methods they have, your class inherits their interface as well, but not their code. Instead methods are created that just forward calls to your method to the equally named method of the included object. The difference between included objects and just encapsulated objects is that you don't have to create the delegation forwards yourself and they don't exist as independent objects that you can pass around, they are part of your object and live and die together with your object (or more technically spoken: The memory for your object and all included ones is created with a single alloc call, same memory block, you just need to init them in your constructor call, while when using real delegates, each of these objects causes an own alloc call, has an own memory block, and lives completely independently of your object).
The language is not so beautiful, but I love the idea behind it :-)