Many websites these days now use simple backgrounds to add to the effect of the design of the website. I and other web designers would always highly recommend using simple background patterns because they load up a lot quicker and aren't distracting. But obviously this depends on the type of website. If it were photography website or a photography portfolio, then go ahead, use a whole picture as a background. It's a great way to show off your work.
Subtle Patterns, a website solely made for sharing minimal patterns is a great resource for downloading material for websites.
However these patterns don't just have to be for websites, you could use them in whatever you like. Whether it was a poster or a print publication. The patterns can be freely used in both personal and commercial projects.