What are the cheapest sites to find hostels around the world to book?

It depends.

1. The prices listed on HostelWorld and HostelBookers are dependent on the hostel themselves, not the website. If it's cheaper on HostelBookers, it's because that's what the hostel was aiming to do. It's not because of HostelBookers themselves. Second thing you need to understand about this is that HostelWorld has bought out HostelBookers not too long ago so essentially it's all going to become the same company as things start to merge more.

2. If you are traveling to SE Asia for example, you're less likely to find hostels and more likely to find locally owned small guesthouses. Many of these places are not listed on hostel websites.

3. During low season in many destinations, you have a better chance in just showing up and negotiating a price. But during high and peak season, you really need to book in advanced otherwise walk-in price is higher if you can even find a room at all.

4. It really depends on where you are going. I had great luck during low season just showing up to many places in SE Asia. I was not so lucky in Europe though. Either way, it's not going to affect your service because you showed up or booked on a website.

Safe travels.

Hostelbookers - not quite as big as hostelworld, but most of the same popular hostels, and they claim to be about 8% cheaper, on average.

I assume you're after global sites - if you're wanting a Colombian one, a Scottish one and a South African one, you'll have to ask separate questions or it'll be considered too broad.