Personally I use a few different size, 1920 x 1080px and I think our latest templates are 2000 x 1600px they dont have to be that big it really depends on whether you care about those on bigger screens and those on smaller screens, personally I tend to keep most of the design close to the middle around the sides of it so people on smaller screens can still see it although they shouldnt care so much for seeing background images on any websites, backgrounds are really better on bigger screens.