I took the liberty of using Dmitry’s pattern and made a version without perforation.
Source Atle Mo
A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.
Source Firkin
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
From a drawing in 'Royal Ramsgate', James Simson, 1897.
Source Firkin
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Adapted from a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Abstract Geometric Monochrome Pattern Prismatic No Background
Source GDJ
Basket Fibers, Basket Texture, Braid Background style CC0 texture.
Source 1A-Photoshop
Colour version of the original pattern.
Source Firkin
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen
Small dots with minor circles spread across to form a nice mosaic.
Source John Burks
It has waves, so make sure you don’t get sea sickness.
Source CoolPatterns
Cubes as far as your eyes can see. You know, because they tile.
Source Jan Meeus
Colour version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Seamless Background For Websites. It has a texture similar to cork-board.
Source V. Hartikainen
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
Run a restaurant blog? Here you go. Done.
Source Andrijana Jarnjak
A monochrome pattern from a tile that can be had by selecting the rectangle in Inkscaope and using shift+alt+i
Source Firkin