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
Dark Denim #29
 Dark  CC BY-SA 3.0

A dark denim looking pattern. 145×145 pixels.

Source Atle Mo

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

Floral background 2@2X #430
 Wall  CC 0

Background formed from the original with an emboss effect

Source GDJ

Background pattern 308 (colour 4) #1868
 Green  CC 0

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

Source Firkin

Background pattern 227 (colour 5) #2310
 Colorful  CC 0

A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.

Source Firkin

Prismatic Dots Background 8@2X #516
 Noise  CC 0

Prismatic Dots Background 8

Source GDJ

Element of beach pattern with background #254
 Noise  CC 0

Element of beach pattern with background.

Source Rones

Vintage pattern #1960
 Grid  CC 0

Formed from a tile based on a drawing from 'Viaggi d'un artista nell'America Meridionale', Guido Boggiani, 1895.

Source Firkin

Fancy Deboss@2X #178
 Fabric  CC BY-SA 3.0

Luxury pattern, looking like it came right out of Paris.

Source Daniel Beaton

Rough Cloth #312
 Fabric  CC BY-SA 3.0

More tactile goodness. This time in the form of some rough cloth.

Source Bartosz Kaszubowski