A smooth mid-tone gray, or low contrast if you will, linen pattern.
Source Jordan Pittman
Hey, you never know when you’ll need a bird pattern, right?
Source Pete Fecteau
People seem to enjoy dark patterns, so here is one with some circles.
Source Atle Mo
Sharp diamond pattern. A small 24x18px tile.
Source Tom Neal
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
One more in the line of patterns inspired by Japanese/Asian styles. Smooth.
Source Kim Ruddock
Prismatic Geometric Pattern Variation 2 With Background
Source GDJ
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Feel free to use this seamless background texture as a background on a web site. It's colored in a light pink color and is seamlessly tile-able.
Source V. Hartikainen