Maybe this is like asking why Windows is popular, or why Buick is popular, but... why is MySQL popular?
I wouldn't be able to use it anyway because we use XML types in our databases. But most of the things I've ever heard are bad things about MySQL. For example, at one point the developers didn't think that foreign keys were useful, and actually wrote defenses of not having them.
I haven't used MySQL for a production tool in a while, so is it purely speed that brings people to MySQL?
I guess the benchmark I think of is, "Would I trust my money to a bank using MySQL?" Would you trust that bank? If so, why?