To get the repeating unit, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
This is the third pattern called Dark Denim, but hey, we all love them!
Source Brandon Jacoby
A free background tile with a pattern of pink bump dots. This background tile is sweet! Moreover, it's designed for use as website backgrounds.
Source V. Hartikainen
Pattern produced in Paint.net using the Vibrato plug-in.
Source Firkin
A version without colours blended together to give a different look.
Source Firkin
Prismatic Floral Background No Black
Source GDJ
It looks like a polished stone surface to me. Download it for free, as always.
Source V. Hartikainen
Your eyes can trip a bit from looking at this – use it wisely.
Source Michal Chovanec
Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.
Source Firkin
Prismatic Polka Dots 3 No Background
Source GDJ
Alternative colour scheme. Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
A seamlessly tile-able grunge background image.
Source V. Hartikainen
Seamless Olive Green Web Background Image
Source V. Hartikainen
Prismatic Groovy Concentric Background 3 No Black
Source GDJ
Psychedelic Geometric Background No Black
Source GDJ
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Sharp but soft triangles in light shades of gray.
Source Pixeden