Rafflecopter - King of Giveaways
This is a company most people have heard about for giving away things through sweepstakes or other systems. The thing about it from an author perspective is that it can be expensive to get all of the features you want.
That's why in many cases multiple authors will band together to use programs like this. It increases visibility and helps cut down on the cost of entry for something like this, and the benefits are tremendous.
There is a free option for giveaways, but it is incredibly limited about what you can offer and difficult to showcase, but you can use this for a month by paying a fee and then cancel it.
Ease of Use
It is incredibly easy to build a giveaway and share it, though making it go viral is something else entirely. You generally need to pay to have images and more options to signup, but you can certainly run a free giveaway without much effort.
This can easily break the bank if you aren't careful. My advice would be to find other like-minded authors and work together on something like this.
You can give books away, but you will get a lot more traction on giving away gift cards or other prizes. The thing is, you want people to buy your books, not just win a free copy, and the hope of 'winning' a copy might actually turn people away.
Big ticket products are also great for promotion, but to help with international distribution you can promote a big item, but give the prize as a gift card so they can 'buy' the item. Not all countries will have the item you are trying to promote.
This is much like gleam.io. Both companies do a great job of giving away products and making it easy for people to enter. If you are at the stage that you want to give stuff away, then research both companies and decide if this is the route you want to go.
Don't put only half effort into it, though, because if you aren't able to gain a lot of traction it can be a costly venture with very little gain.