There are numerous websites with free patterns, some specifically for hooked rugs and others that are easily adapted to hooking. Try P&B Textiles - meant for quilting, but many would make lovely rugs. I particularly like Bella's Blooms and there are many geometrics that would be great either in hit-or-miss or in a planned colour scheme. Here's a page with 1295 sites, all offering free patterns, and categorized by theme, holiday or subject [Fish, Frogs & Bugs or Snowmen, for example]. Again, this is a quilting site, so some of the paper piecing patterns might not translate so well, but for anyone who is shy of drawing their own pattern, these are treasure troves!
Donna Hrkman, a talented rughooker, shares a free snowman pattern on her site: at Blue Ribbon Rugs; it may change seasonally. Her Women of the Congo rug was featured in RHM/ Rug Hooking Magazine (Jan/Feb 2006) and is a powerful work of art and compassion.
Stained glass patterns are also ideal for hooking; though this 'fantasy' site has a strong cartoon and juvenile bent, it does have many free stained glass patterns! And yet more, at Spectrum, where you are asked to log in with a password, but it's quick and easy, and free patterns are searchable by category.
For some fun free primitive patterns, Jennie Baer at Homeberries has 'freebies' - just click on the category you are looking for - seasons, ornies, nursery rhymes and everyday (e.g. "A Happy Home is Early Heaven"). They are meant for embroidery but I think would make sweet mats.