I haven't used the e-book option yet because of the various format wars.

But I have downloaded audio books from my library system. They use both Overdrive and Ingrams MyiLibrary audio. I've had success downloading titles and even getting them to work on my Sony MP3 player. Heck, that's more than I can say for Audible.com as the one free title I downloaded from them can't play on my Sony.
However, sometimes the searches can be very frustrating, especially in the Ingrams audio catalog. For example, searching by category under the Ingrams audio catalog is a nightmare as there are many categories with no titles, while some general categories (such as Fiction) can have hundreds of titles. (Why can't they group the books under more than one category anyway? It's not as if they're using physical shelf space.) For example, there are something like ten categories simply called "Fiction" and even several called "No category" or something like that.

There are also dozens of categories like "Fiction -- Ghosts" and "Fiction -- Cats" and "Fiction -- Coming of Age" and "Fiction -- Goldfish." OK, I'm kidding about the goldfish, but you get the idea.

But when I search these categories, I find that they have no books listed. Sigh! If you search by author name or title, you're in better luck. However, I couldn't find anything by Stieg Larsson in a search, but that's because they had him listed as "Steven Larsson."