Perhaps a Google project like the books scanning they did? That would be really cool.
* it doesn't have to be non-profit tech org of course (I did mention google's book project after all), but finding a for-profit that would make things freely available might be a challenge in itself since the costs would not likely be low, either for development or infrastructure/maintenance.
The library systems in the last two places I lived both subscribed to services where when you put your library card number in, you could browse the archives of hundreds of newspapers, magazines and journals. Some of them going back into the 1800's.
There's also "Chronicling America" - it's a federal government (Library of Congress) web site that has full page scans of 500 different newspapers from 1836-1922. Free and open to everyone in the world: https://chroniclingamerica.loc.gov