Carbon Fiber v2@2X #106
 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
Background pattern 306 (colour 6) #1878
 Colorful  CC 0

Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.

Source Firkin

Candyhole #356
 Light  CC BY-SA 3.0

It’s a hole, in a pattern. On your website. Dig it!

Source Josh Green

Fabric pattern 3 (colour 5) #2383
 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

White Sand@2X #20
 Light  CC BY-SA 3.0

Same as gray sand but lighter. A sandy pattern with small light dots, and some angled strokes.

Source Atle Mo

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

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

Source Marco Slooten

Cubes #133
 Light  CC BY-SA 3.0

This reminds me of Game Cube. A nice light 3D cube pattern.

Source Sander Ottens

Abstract Tiled Background Extended 8 #519
 Noise  CC 0

Abstract Tiled Background Extended 8

Source GDJ

Paper 1 #15
 Paper  CC BY-SA 3.0

A slightly grainy paper pattern with small horizontal and vertical strokes.

Source Atle Mo

Diamond pattern (colour 2) #2284
 Green  CC 0

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

Source Firkin

Background pattern 252 (colour 3) #2160
 Green  CC 0

Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.

Source Firkin

"Glossy Pink Fur", Pink Background Pattern #1235
 Pink  CC BY-SA 3.0

Here's a quite bright pink background pattern for use on websites. It doesn't look like a real fur, but it definitely resembles one.

Source V. Hartikainen

Background pattern 238 (colour 3) #2227
 Blue  CC 0

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

Source Firkin

Small Crosses@2X #116
 Stripes  CC BY-SA 3.0

Sharp pixel pattern looking like some sort of fabric.

Source Dmitry

Rice Paper 2@2X #341
 Paper  CC BY-SA 3.0

One can never have too few rice paper patterns, so here is one more.

Source Atle Mo

Background pattern 339 #1709
 Dark  CC 0

The tile this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i

Source Firkin

Retro Circles Background 8 No Black@2X #438
 Dark  CC 0

Retro Circles Background 8 No Black

Source GDJ