List of Sites Offering Free WordPress Themes 2015:

Freebies! What an inviting word. Especially when it comes to WordPress development, as the vast majority of website owners and bloggers use WordPress today.
WordPress has always been free as a platform, but it is still a challenge to build a good-looking WordPress site at no additional cost. Why? First of all because free hosting is not always reliable, so you will need to spend at least $10 a month to get a decent hosting plan.
As for the design of your WordPress site, there are several options available. The first, and most expensive, one would be to hire a designer to create a custom-made template for your site. The result will be a great-looking site exactly the way you want it, but the cost can add up to several thousand dollars.

Purchasing a premium theme is another good option, but if you are just getting started you might not feel comfortable spending $100 or so on the design of your site.
For those in that position, getting a free WordPress theme is the best option. And don’t worry, you won’t need to compromise in quality, there are several great-looking free WP themes around. You just need to search in the right places.
The first obvious stop if the official Theme Directory. There you’ll find thousands (literally) of themes available. Apart from the official directory, though, there are many sites that offer high quality themes. Below you’ll find a list of them: