In the US, we have an online rental store called GameFly. They deliver games to your house after two to three days of ordering them, which is quite fast. Sometimes, you won't receive a game due to shipment issues, but they will send you a replacement as soon as you report it to them. They have a great selection of games, and it requires you less than twenty dollars a month to stay subscribed to them. If you like a game that you borrowed, then you can actually keep it by paying them some additional fees. Usually, it costs you around sixty dollars to purchase a new game, but with that amount of money, you'll be able to stay subscribed to them for three straight months and play as much games as you like!
I've given their service a try for an entire month last year, and it was a great experience. (: