Green Fibers@2X #92
 Dark  CC BY-SA 3.0

The green fibers pattern will work very well in grayscale as well.

Source Matteo Di Capua

 More Textures
Prismatic Polka Dots Mark II 3 No Background #534
 Noise  CC 0

Prismatic Polka Dots Mark II 3 No Background

Source GDJ

Micro Carbon #7
 Carbon  CC BY-SA 3.0

Three shades of gray makes this pattern look like a small carbon fiber surface. Great readability even for small fonts.

Source Atle Mo

Background pattern 230 (colour 2) #2302
 Green  CC 0

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

Source Firkin

Fabric pattern (colour 6) #2397
 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

Dark Blue Gray Wallpaper Texture #901
 Stripes  CC BY-SA 3.0

This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!

Source V. Hartikainen

Background pattern 256 #2139
 Red  CC 0

Remixed from a design on Pixabay. To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i

Source Firkin

edo pattern-samekomon #2271
 Dark  CC 0

The image depicts an edo-era pattern called "same-komon" or "鮫小紋"which looks like a shark skin.The "same" in Japanese means shark in English.

Source Yamachem

Diamond pattern 2 (colour 4) #2265
 Red  CC 0

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

Source Firkin