To get the repeating unit, select the rectangle in Inkscape and use shift+alt+i
Source Firkin
Here's an yet another background for websites, with a seamless texture of wood planks this time.
Source V. Hartikainen
Green Background Pattern
Source V. Hartikainen
A heavy dark gray base, some subtle noise and a 45-degree grid makes this look like a pattern with a tactile feel to it.
Source Atle Mo
No, not the band but the pattern. Simple squares in gray tones, of course.
Source Atle Mo
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
From an image on opengameart.org shared by rubberduck.
Source Firkin
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
The image depicts meshed silhouettes of various things.The original image is an OCAL clipart called "Enter FOSSASIA 2016 #IoT T-shirt Design Contest" uploaded by "openclipart".Thanks.
Source Yamachem
From a drawing in 'Sun Pictures of the Norfolk Broads', Ernest Suffling, 1892.
Source Firkin
Derived from a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
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
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Real Sailor-Songs', John Ashton, 1891.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
From a drawing in 'Kingsdene', Maria Fetherstonehaugh, 1878.
Source Firkin
A dark brown fabric-like background texture with seamless pattern of winding stripes.
Source V. Hartikainen
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Zero CC tileable ground (#2) cracked, crackled texture, made by me. CC0
Source Sojan Janso
A seamless pattern with wide vertical stripes colored in pale yellow.
Source V. Hartikainen
A free seamless background texture of "timber wall" (colored in dark brown).
Source V. Hartikainen
A brown metallic grid pattern layered on top of a dark fabric texture. It should look great when using as a tiled background on web pages, especially blogs.
Source V. Hartikainen