I'm sorta unconvinced we'll actually see any benefit. Humans are notoriously picky about their privacy; The ability to get black-box data for insurance purposes has been around for years, but most people would rather not, for good reason, have their insurers poking around their driving habits. I expect some backlash against cars collecting this data on their driving neighbors. What if the self-driving car isn't involved in an accident, but witnesses one? Can the courts subpoena google for the two driver's locations and velocities? That will be a fantastic NYT headline: "Are Google cars spying on you?"
Look at public health data. There's a vast goldmine of data that could be collected, that could track, trace, and storm-warning diseases, but that is for legal reasons hidden behind a confidentiality barrier. I'd like it to be a simple check if any of your partners were STD positive; This is currently information that is hard to get reliably (Sure, your partner can hand you test results, but not verifiable ones; The clinic won't attest to it if you call to reference your partner's results, so you can never be certain it's not a clever photoshop). This is data that has direct, tangible impact on those around you, and in many states it is a crime to not reveal certain STDs. Still, these spread, because we're afraid of making the STD-infected social pariahs, and I can't see a world where we don't have the same problem with bad drivers.