The best (price-wise) game rental service I've seen so far has been GamezNflix Game Rental, with prices clocking in as follows: 

2 Out at a Time / $9.75 each month
3 Out at a Time / $12.75 each month

In addition, as part of their military discount program, GameZnFlix offers service-members past and present a 1-month FREE Membership.  Yes if you or any of your family members have served in uniform you are entitled to a FREE Membership

Steps: 

1.  Click here GamezNflix Game Rental

2.  Use the coupon code: emmys

For Military program sign up:

1.  Click here GamezNflix Military Program Discounts

 

[Thanks Stryker115, militarygamez]