Jacqui Shine has published a piece at Chronicle Vitae where she describes some of the ways in which academics without a university affiliation can access certain library resources. Based on a variety of conversations over the past few years, this seems to be the issue that offers the greatest challenge to independent scholars. I am still cautiously optimistic that, if the current trend towards open-access publishing continues, library access will be less of a barrier to entry over time. However, the extent to which relevant resources are openly available varies from field to field.
Shine’s article mentions a number of resources that I was previously unfamiliar with, so if you’re looking for ideas, check it out. Her list is especially rich on the humanities side — lots of ideas about accessing old newspapers, for example. She put in a call for more ideas in the comments, so hopefully even more stuff will show up there.