It feels like companies pretend that unpaid internships are important for a resume just so they can have people slave away at their own cost year after year...

Yeah, it's the whole exposure BS

Depends on what you are capable of and how much they're investing in you. If you get a mentor and can't be trusted any real work, then I totally understand them not giving you money. But if you can actually get shit done, you should be paid. Use your success stories and achievements on the business level as arguments in a serious talk. Try to make your work effect measurable in business value and money. For example if you saved another developer 2h of work, then you won the company what that guy would cost them for 2h. If you increased the development speed by 0.1%, then that probably raises the revenue by 0.03% or so. Calculate that against actual numbers (they are usually public)

@bendr in my understanding you basically pay for private lessons with your work. Consider this: some people work hours in shitty jobs in order to pay for tutorials, books, school and private teachers. An internship is basically the same except the borders of paying and being paid are more blurry