I found this great list a few days ago:
(see article for links)
If there aren’t any options where you live, there a few libraries that offer cards to out-of-state residents for an annual fee.
Libraries that offer library cards for non-residents
The Brooklyn Public Library has a wide selection of ebooks, however library cards for non-residents will set you back $50 a year.
The Free Library of Philadelphia is another option. They offer library cards to non-residents for $35 a year.
The Fairfax County Library in Virginia offers a library card to non-residents for $27 a year.
The Houston Public Library in Texas offers a library card to non-residents for $20 for six months or $40 a year.
Another option is the Charlotte Mecklenburg Library in North Carolina. They offer library cards to non-residents for $45 per year, $35 for adults 62 years and older.
The Monroe County Library in New York offers cards to non-residents for $45 per year.
More libraries with non-resident cards can be found here »
The libraries above all have a decent selection of titles to choose from, but make sure they have what you’re looking for and double-check to see how long the wait is before shelling out any dough.