Small repeating images that create a background pattern are something I use in every website I design. Background Image Generator by SiteOrigin is my favorite tool for creating these patterns. They give users the ability to use ANY hex color (There are 16,777,216 hex colors) to change the color of their simple background patterns. Their customizable background images come from another great website, Subtle Patterns. They have hundreds to choose from. You can also add filters, change the intensity of the pattern and add noise to the background image. The patterns are well optimized so they load fast on websites.
There are other background image generators out there, but none with the great features Background Image Generator provides. It's also free so you can't beat that! Check out my portfolio to see the many different patterns I've used on clients websites or contact me today to learn more.