Dark Blue Gray Wallpaper Texture #901
 Stripes  CC BY-SA 3.0

This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!

Source V. Hartikainen

 More Textures
Prismatic Polka Dots 3 No Background #528
 Noise  CC 0

Prismatic Polka Dots 3 No Background

Source GDJ

Seamless Prismatic Pythagorean Line Art Pattern No Background #569
 Light  CC 0

Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).

Source GDJ

Robots@2X #126
 Dark  CC BY-SA 3.0

And some more testing, this time with Seamless Studio. It’s Robots FFS!

Source Seamless Studio

Background pattern 230 (colour 3) #2303
 Green  CC 0

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

Source Firkin

Background pattern 8 (black) #209
 Dark  CC 0

Black version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net

Source Firkin

Prismatic Abstract Line Art Pattern Background #565
 Dark  CC 0

Prismatic Abstract Line Art Pattern Background

Source GDJ

Seamless Colorful Floral Pattern Background #256
 Fabric  CC 0

PDP

Source GDJ

Background pattern 252 (colour 5) #2158
 Light  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

Retro Circles Background 4@2X #421
 Dark  CC 0

Retro Circles Background 4

Source GDJ

45-Degree Fabric #1
 Fabric  CC BY-SA 3.0

Medium gray fabric pattern with 45-degree lines going across.

Source Atle Mo

Prismatic Groovy Concentric Background 4 #461
 Noise  CC 0

Prismatic Groovy Concentric Background 4

Source GDJ

Parquet flooring pattern (colour 3) #2425
 Pink  CC 0

A seamless pattern recreated from an image on Pixabay. It is reminiscent of parquet flooring and is formed from a square tile, which can be recovered in Inkscape by selecting the ungrouped rectangle and using shift-alt-I together.

Source Firkin