You can check the Top 100 Free Kindle eBooks to see if there might be a new book to read over the weekend. Make sure that you are looking in the column for the free ones.
Here are a few of them listed there right now: (it’s updated hourly)
(Thanks, Give Me Neither!)
Keep in mind that prices flip fast on Amazon so be sure it states “Free” or $0.00 before you buy it. Also, remember that you don’t need a Kindle to read them as you can download an App to read it on your iPhone, Droid, Blackberry, PC or Mac.