Squares@2X #303
 Dark  CC BY-SA 3.0

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

Source Jaromír Kavan

 More Textures
Zig-zag pattern 4 #2415
 Grid  CC 0

A seamless pattern based on a rectangular tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.

Source Firkin

Floral Pattern Background 3 #218
 Noise  CC 0

PDP

Source GDJ

Prismatic Abstract Geometric Background 2 #268
 Noise  CC 0

Prismatic Abstract Geometric Background 2

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

Part of Bayeux Tapestry 2 #2451
 Noise  CC 0

From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.

Source Firkin

Retro Squares Background #414
 Noise  CC 0

Retro Squares Background

Source GDJ

Background pattern 259 (colour 4) #2131
 Green  CC 0

Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.

Source Firkin

Art nouveau tile pattern remix #2529
 Green  CC 0

A seamless pattern formed from a modified version of rwwgub's tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.

Source Firkin

"Grunge-Like" Background Pattern #1126
 Grunge  CC BY-SA 3.0

Background pattern made in "Grunge-Like" style. Available in both SVG and JPG formats. Edit to your needs then click the download button.

Source V. Hartikainen

Prismatic Curved Diamond Pattern 6 No Background #545
 Dark  CC 0

Prismatic Curved Diamond Pattern 6 No Background

Source GDJ

Background pattern 309 (colour 4) #1863
 Green  CC 0

Design drawn in Paint.net, vectorised using Vector Magic and finished in Inkscape.

Source Firkin

Checkered Light Emboss@2X #281
 Grid  CC BY-SA 3.0

Sort of like the Photoshop transparent background, but better!

Source Alex Parker