Examples would be offering free uploads of images up to X megs per month but charging X cents per image after. Or the ability to create more than X number of interest groups. Micro-payments advantage also is that the service can charge strategically to offset some of the higher serving costs of certain functionality, eg., storage.
The advantage of micro-payments over freemium is that with freemium the user may be very hesitatant to lock into $10 a month -- but might be willing to pay more ad hoc for enhanced functionality that over time they really want to use. The key of course is the network must be very smart about pricing and what actions are charged, and still provide an exceptional experience for free.
The system is working well in various online games (buying powers) and cell phone networks ... could it work well in a social network? I expect to see more attempts for sure.