• It's integral to the code (if I want it to be), so I'm less likely to forgot to update doc when I change the code.
• POD can be exposed at run-time using modules like Pod::Usage -- so with just a little bit of planning, the documentation can double as help/manpage info for your users.
• POD doesn't require any extra tools, which is nice if you're developing on and deploying to multiple systems.
• It's easy to convert POD to plain text, HTML, and a variety of other output flavors.
• Various Pod::* modules give me other ways to manipulate the POD contents. For example, I can write a pre-deployment check that makes sure my POD contains correct copyright notices and so on.

Of course, if there's something better out there I'd love to know about it too. But looking at the doc for RoboDoc -- I haven't actually used it -- makes it seem like it offers POD-like functionality but not a lot of extras that would compel me to switch.