I'm a librarian who loves anime, manga, and reading a wide variety of genres.
My town's public library is tiny and underfunded, but just this past weekend I learned that even they have an e-book lending service. Not Overdrive, which I'm familiar with through my mom's library, but something called Freading. I'd be trying it already if my library card number didn't keep coming up as "invalid." Hopefully someone will be able to help me sometime tomorrow.
I spent some time browsing the site. Users get a certain number of tokens per week (I won't know how many until my library card number works and I can log in), which can be used to "pay" for checkouts. Books cost anywhere from one to four tokens, and I think they can be checked out immediately, with no waiting list. The selection seems to be sadly lacking, but I still found quite a few books I'd love to read. The site's search functions are awful. Depending on how I searched for Kage Baker, I sometimes found one book, or two books, or one completely different book.
I vaguely remember Freading being mentioned at a library conference I attended a year or two ago, although I can't remember if the presenter liked or disliked its model as compared to Overdrive's.
As a library user, I'm happy to discover that there is actually an e-book lending service in my area. Here's hoping I can figure out how to use it.