The advantage of prototypal inheritance is that it potentially allows fancy metaprogramming in a straightforward way because the prototype chain is easily manipulated. This is a rather academic advantage because metaprogramming is the wrong answer 99% of the time. As an example, you could have a Javascript Key-Value Observer style data manipulation layer with a special DSL that transparently switched between a local SQLite backing when offline and a REST based server store when online via prototype swapping. I’m not sure it’s the best way to do this, but it’s the best I can come up with this late. It’s not the sort of thing you generally want to do in project code since this sort of indirection is hell to debug once you start getting it going on multiple layers, but it’s not bad when you keep it in a library.
Another less helpful advantage is that it allows you to design your own class system. I say less helpful because more or less all javascript libraries have their own slightly incompatible approach to how ‘classes’ are put together.
There are a lot of people replying who are mixing the inheritance model with the languages implemented in that model. The fact that javascript is dynamic and weakly typed and thus hard to tool has nothing to do with it being a prototypal language.