Background pattern 250 (colour 2) #2170
 Blue  CC 0

To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.

Source Firkin

 More Textures
Part of Bayeux Tapestry 1 #2452
 Noise  CC 0

From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.

Source Firkin

Prismatic Groovy Concentric Background 5 No Black #467
 Dark  CC 0

Prismatic Groovy Concentric Background 5 No Black

Source GDJ

Fabric pattern (colour 4) #2399
 Fabric  CC 0

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

Background pattern 308 (colour 5) #1869
 Blue  CC 0

Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.

Source Firkin

Dark Denim@2X #373
 Dark  CC BY-SA 3.0

Thin lines, noise and texture creates this crisp dark denim pattern.

Source Marco Slooten

Carbon Fiber v2 #105
 Carbon  CC BY-SA 3.0

One more updated pattern. Not really carbon fiber, but it’s the most popular pattern, so I’ll give you an extra choice.

Source Atle Mo

Medic Packaging Foil #376
 Light  CC BY-SA 3.0

8 by 8 pixels, and just what the title says.

Source pixilated

Small Crosses #115
 Stripes  CC BY-SA 3.0

Sharp pixel pattern looking like some sort of fabric.

Source Dmitry

Cross Stripes@2X #48
 Dark  CC BY-SA 3.0

Nice and simple crossed lines in dark gray tones.

Source Stefan Aleksić