"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

 More Textures
Random Binary Background #274
 Light  CC 0

Random Binary Background

Source GDJ

Background pattern 238 (colour 2) #2228
 Green  CC 0

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

Source Firkin

Retro Circles Background 5 #424
 Noise  CC 0

Retro Circles Background 5

Source GDJ

Prismatic Polka Dots Mark II 2 No Background #532
 Noise  CC 0

Prismatic Polka Dots Mark II 2 No Background

Source GDJ

Transparent Square Tiles@2X #299
 Grid  CC BY-SA 3.0

The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.

Source Nathan Spady

Stripy checkerboard pattern 2 #1767
 Dark  CC 0

Simple combination of stripy squares with their negatively coloured counterparts

Source Firkin

Tessellation 16 (colour 4) #2212
 Green  CC 0

The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.

Source Firkin

Project Papper@2X #120
 Paper  CC BY-SA 3.0

Light square grid pattern, great for a “DIY projects” sort of website, maybe?

Source Rafael Almeida

Exclusive Paper@2X #24
 Light  CC BY-SA 3.0

Paper pattern with small dust particles and 45-degree strokes.

Source Atle Mo