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
Background pattern 226 (colour 2) #2320
 Green  CC 0

A seamless pattern from a tile made from a jpg on Pixabay. To get the tile select the rectangle in Inkscape and use shift-alt-i.

Source Firkin

seigaiha subtle color #2278
 Pink  CC 0

This is a remix of "blue wave-seigaiha".I hope this subtle color version of Seigaiha would be suitable for background .

Source Yamachem

Starting Diamond Shape@2X #138
 Light  CC 0

Simple blue and line to mix.

Source SliverKnight

Seamless Core Pattern 10 #171
 Dark  CC 0

Seamless Core Pattern 10

Source GDJ

Prismatic Hypnotic Pattern No Background #571
 Noise  CC 0

Prismatic Hypnotic Pattern No Background

Source GDJ

Robots@2X #126
 Dark  CC BY-SA 3.0

And some more testing, this time with Seamless Studio. It’s Robots FFS!

Source Seamless Studio

gourd seamless pattern #2277
 Brown  CC 0

The image depicts a seamless pattern which includes hexagonally-aligned gourds with BG in light-brown.

Source Yamachem

White Texture #131
 Light  CC BY-SA 3.0

Not the most creative name, but it’s a good all-purpose light background.

Source Dmitry

Vintage Elegant Floral Background #257
 Fabric  CC 0

PDP

Source GDJ

Prismatic Groovy Concentric Background 2@2X #454
 Noise  CC 0

Prismatic Groovy Concentric Background 2

Source GDJ

Spirals pattern #1994
 Colorful  CC 0

Uses spirals from Pixabay. To get the basic tile select the rectangle in Inkscape and use shift+alt+i

Source Firkin

Background pattern 309 (colour 4) #1863
 Green  CC 0

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

Source Firkin

Dark Brown Wood Background (Tile-able) #886
 Wood  CC BY-SA 3.0

Tile-able Dark Brown Wood Background. Feel free to use it as a background image in your designs or somewhere on the web. By the way, the color seems to be close to Coffee Brown.

Source V. Hartikainen