I recently attended an interview and they asked me the question "Why Interfaces are preferred over Abstract classes?"
I tried giving a few answers like:
That interview question reflects a certain belief of the person asking the question. I believe that the person is wrong, and therefore you can go one of two directions.
The answer that they want, well, the other posters have highlighted those incredibly well. Multiple interface inheritance, the inheritance forces the class to make implementation choices, interfaces can be changed easier.
However, if you create a compelling (and correct) argument in your disagreement, then the interviewer might take note. First, highlight the positive things about interfaces, this is a MUST. Secondly, I would say that interfaces are better in many scenarios, but they also lead to code duplication which is a negative thing. If you have a wide array of subclasses which will be doing largely the same implementation, plus extra functionality, then you might want an abstract class. It allows you to have many similar objects with fine grained detail, whereas with only interfaces, you must have many distinct objects with almost duplicate code.
Interfaces have many uses, and there is a compelling reason to believe they are 'better'. However you should always be using the correct tool for the job, and that means that you can't write off abstract classes.