I'm currently reading A Clash of Kings via Overdrive. I also read the first four books of the Culture series, a Canticle for Liebowitz, the Forever War, the Martian (the waitlist was epic for this one--good thing it is a quick read), and the Hyperion Cantos.
Amusingly, my library offers Game of Thrones in two formats: a 4 book set with the first 4 books of A Song of Ice and Fire, and a 5 book set that also includes the most recent one. I thought they were awfully optimistic about my ability to read all 5 books of A Song of Ice and Fire in 3 weeks.
Overdrive has a couple of quirks. The first is that the "online reading" mode sucks ass. Never use it. Always download the book to your device. Trust me. The other is that renewals are handled somewhat awkwardly. The book still self destructs on your device and you have to download it again every time you renew. It does at least remember your place in the book when you do this.
The best thing about Overdrive is that it is on my phone, so it is always with me. If I ever find myself with time to kill, I can just fire it up and read a few more pages. It's not quite as nice as a dedicated e-reader, but the convenience factor is huge. I liken it to the way cameraphones killed off point and shoot cameras. They aren't as good, but the convenience factor outweighs the downsides. How many times have you been stuck in a waiting area going "I should have brought a book"? Never again.