Everyone has probably heard of NetFlix, the company that puts a DVD rental store in your mailbox. But, a little newer, and growing quickly in popularity, is a collection of online video game rental companies. They work much the same way as NetFlix. You sign up online, setup a list of games you'd like to play, and wait for them to show up in your mailbox. When your done playing, drop it the mailbox, and wait for your next one to show up. Shipping both ways is paid for by the game rental company. Convenient and cheaper than buying and renting from your local video / games store.
The are a variety of plans to consider, when you choose to rent video games online. The main factor distinguishing the plans, is the number of games you are allowed to have checked out at one time. The more games checked out, the higher your monthly fees. Plans typically allow from one to six games out at a time. The severity of your gambling addiction will of course determine which plan you sign up for. I would personally stay away from the one game out at a time plan. Having a two or more plan, guarantees you will always have at least one rental game in your console, even if one is in transit.
The other thing I should mention, is that console games are the only games you can rent. Due to illegal copying issues, PC games have never really found their way into the rental business. But, most companies do carry games for just about any console you might have. Wii, Xbox, Xbox 360, PS, PS2, PS3, PSP, Nintendo DS, GameBoy Advance, and even the Nintendo Game Cube. Some companies do offer videos as well, but it's best to browse their selection, and make sure they have the kind of titles you would be interested in.
Another safety net that most companies provide, is the free trial. That makes signing up a pretty easy decision. You could even sign up with more than one company at a time, and give them a real good comparison. It will not cost you anything, and only make you a more informed consumer.