Small Crosses #115
 Stripes  CC BY-SA 3.0

Sharp pixel pattern looking like some sort of fabric.

Source Dmitry

 More Textures
Small Crosses@2X #116
 Stripes  CC BY-SA 3.0

Sharp pixel pattern looking like some sort of fabric.

Source Dmitry

Background pattern 251 (colour 2) #2166
 Yellow  CC 0

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

Source Firkin

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

Prismatic Groovy Concentric Background 5@2X #466
 Dark  CC 0

Prismatic Groovy Concentric Background 5

Source GDJ

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

Felt #300
 Wall  CC BY-SA 3.0

Got some felt in my mailbox today, so I scanned it for you to use.

Source Atle Mo

Retro Squares Background 4@2X #419
 Dark  CC 0

Retro Squares Background 4

Source GDJ

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

Prismatic Groovy Concentric Background 5 #465
 Dark  CC 0

Prismatic Groovy Concentric Background 5

Source GDJ

Starring@2X #586
 Dark  CC BY-SA 3.0

If you need stars, this is the one to get.

Source Agus Riyadi

"Dark Brick Wall", Background Pattern #1024
 Stone  CC BY-SA 3.0

Like the name suggests, this background image consists of a pattern of dark bricks. It may be an option for you, if you are looking for something that looks like a brick wall for use as a background on web pages. It's not a masterpiece, but looks pretty nice when is tiled.

Source V. Hartikainen

Background pattern 328 (colour 4) #1798
 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 2 (colour 4) #2393
 Fabric  CC 0

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