"Polished Stone", Gray Background Pattern #1053
 Stone  CC BY-SA 3.0

A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).

Source V. Hartikainen

 More Textures
Fabric pattern (colour 3) #2400
 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

Prismatic Groovy Concentric Background@2X #450
 Noise  CC 0

Prismatic Groovy Concentric Background

Source GDJ

Triangles #127
 Dark  CC BY-SA 3.0

Dark and hard, just the way we like it. Embossed triangles makes a nice pattern.

Source Ivan Ginev

"Green Rhombuses", Seamless Background Pattern #1336
 Green  CC BY-SA 3.0

A free green background pattern with a pattern of rhombuses on a seamless texture. Feel free to use it as a tiled background image on your web site.

Source V. Hartikainen

MBossed@2X #194
 Grid  CC BY-SA 3.0

Embossed lines and squares with subtle highlights.

Source Alex Parker

Old Mathematics #43
 Stripes  CC BY-SA 3.0

This one takes you back to math class. Classic mathematic board underlay.

Source Josh Green

Fabric 1@2X #10
 Light  CC BY-SA 3.0

Semi-light fabric pattern made out of random pixels in shades of gray.

Source Atle Mo

Bright Multicolored Floral Background #559
 Noise  CC 0

Bright Multicolored Floral Background by Karen Arnold from PDP.

Source GDJ

Green Fibers #91
 Dark  CC BY-SA 3.0

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

Source Matteo Di Capua

Dark Denim #29
 Dark  CC BY-SA 3.0

A dark denim looking pattern. 145×145 pixels.

Source Atle Mo

Retro Squares Background 5 #395
 Dark  CC 0

Retro Squares Background 5

Source GDJ

Always Grey@2X #54
 Dark  CC BY-SA 3.0

Crossing lines with a subtle emboss effect on a dark background.

Source Stefan Aleksić

Prismatic Polka Dots 3 No Background@2X #529
 Noise  CC 0

Prismatic Polka Dots 3 No Background

Source GDJ

Background pattern 314 (colour 3) #1837
 Green  CC 0

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

Source Firkin