This is a seamless pattern of regular hexagon which has a honeycomb structure.
Source Yamachem
Original seamless pattern with an Inkscape filter.
Source Firkin
Orange-red pattern for tiled backgrounds.
Source V. Hartikainen
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
Turn your site into a dragon with this great scale pattern.
Source Alex Parker
The unit cell for this seamless pattern can be had in Inkscape by selecting the rectangle and using shift+alt+i.
Source Firkin
Submitted in a cream color, but you know how I like it.
Source Devin Holmes
Prismatic Abstract Geometric Background 4
Source GDJ
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
CC0 and a seamless pattern from a tile drawn in Paint.net .
Source SliverKnight
Derived from an image that was uploaded to Pixabay by TheDigitalArtist
Source Firkin
A black tile-able background with paper-like texture.
Source V. Hartikainen
A free green background pattern with a pattern of rhombuses on a seamless texture. Feel free to use it as a tiled background image on your web site.
Source V. Hartikainen
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
From a drawing in 'Handbook of the excursions proposed to be made by the Lincoln Diocesan Architectural Society, on the 27th and 28th of May, 1857', Edward Trollope, 1857.
Source Firkin
A repeating background of beige paper with vintage look. Repeats to infinity, as usual.
Source V. Hartikainen
Zero CC tileable hard cover cells, skin like, book texture. 4K, Scanned and made by me CC0
Source Sojan Janso
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
Actually remixed from a pattern on Pixabay. But then noticed a very similar one on Openclipart.org uploaded by btj51q2.
Source Firkin
From a drawing in 'Line and form', Walter Crane, 1914.
Source Firkin
Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
Remixed from a drawing in 'The Canadian horticulturist', 1892
Source Firkin
A free seamless background texture that looks like a brown stone wall.
Source V. Hartikainen