There are a lot of great WordPress themes available for free, but you’ll need to be careful about where you get them from. Bad themes with malicious code can bring down your server, alter links on your website, and cause other unsavory problems.
Free themes from reputable sources can be terrific though. Here’s some of the places I’d check first, with a few example themes from each.
The theme repository on WordPress.org is the largest source of free WordPress themes. All themes go through a detailed code review and safe to use on your site. You can browse the featured themes, popular themes, and newest themes.