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

 More Textures
Prismatic Abstract Geometric Background 2 No Black #445
 Noise  CC 0

Prismatic Abstract Geometric Background 2 No Black

Source GDJ

Decorative divider 198 #2437
 Dark  CC 0

From a drawing in 'Codogno e il suo territorio nella cronaca e nella storia'', Gio and Giarella Cairo, 1897.

Source Firkin

Prismatic Curved Diamond Pattern 3 No Background@2X #540
 Diamond  CC 0

Prismatic Curved Diamond Pattern 3 No Background

Source GDJ

Background pattern 105 #563
 Dark  CC 0

A seamless pattern formed from background pattern 102

Source Firkin

Colourful background #2010
 Colorful  CC 0

Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic

Source Firkin

Fabric pattern (colour 2) #2401
 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

Beige Paper #83
 Paper  CC BY-SA 3.0

This was submitted in a beige color, hence the name. Now it’s a gray paper pattern.

Source Konstantin Ivanov

Real Carbon Fiber #286
 Carbon  CC BY-SA 3.0

Carbon fiber is never out of fashion, so here is one more style for you.

Source Alfred Lee

Diamond pattern (colour 7) #2274
 Red  CC 0

From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.

Source Firkin