I have applied for a card at the Philidelphia library, but a US friend also has allowed me to check out books on her account as long as she doesn't need them. Really neat!
In Sweden we have quite an extensive list of eBooks in our library. Most of them Swedish though. (Not just when it comes to the language, but to the origin.)
We don't ever have to wait for an eBook. It's always available. I think the library buys a certain number of licenses from our Overdrive equivalent, but it's not tied to specific books. When the licenses run out - tough! (They did just before Christmas last year when I had my eyes on a really interesting book about Berlusconi to read during the weekend. Had to wait until after NewYear when they got new licenses.)
Thanks for the tip on the Singapor library! It doesn't hurt to have yet another option!