More Textures
Checkered Light Emboss #280
 Grid  CC BY-SA 3.0

Sort of like the Photoshop transparent background, but better!

Source Alex Parker

Prismatic Rounded Squares Grid 4 No Background #491
 Noise  CC 0

Prismatic Rounded Squares Grid 4 No Background

Source GDJ

Background pattern 306 (colour 5) #1879
 Colorful  CC 0

Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.

Source Firkin

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

Background pattern 267 #2067
 Dark  CC 0

Remixed from a drawing in 'An Index to Deering's Nottinghamia Vetus et Nova', Rupert Chicken, 1899. The unit tile can be had by selecting the rectangle in Inkscape and using shift-alt-i

Source Firkin

Tessellation 16 (colour 2) #2214
 Colorful  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

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

Background pattern 252 #2162
 Dark  CC 0

Recreated from a pattern found in 'Az Osztrák-Magyar Monarchia irásban és képben', 1882. To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i.

Source Firkin

Background pattern 224 (colour 5) #2338
 Colorful  CC 0

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

Source Firkin

Squares #302
 Dark  CC BY-SA 3.0

Dark, square, clean and tidy. What more can you ask for?

Source Jaromír Kavan

Carbon Fiber v2@2X #106
 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

Prismatic Curved Diamond Pattern 2 No Background@2X #539
 Diamond  CC 0

Prismatic Curved Diamond Pattern 2 No Background

Source GDJ