A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
From a drawing of the coat of arms of the Ottoman Empire on Wikimedia.
Source Firkin
You guessed it – looks a bit like cloth.
Source Peax Webdesign
People seem to enjoy dark patterns, so here is one with some circles.
Source Atle Mo
Vector version of a JPG that was uploaded to Pixabay by theasad121
Source Firkin
This one could be the shirt of a golf player. Angled lines in different thicknesses.
Source Olivier Pineda
Small gradient crosses inside 45-degree boxes, or bigger crosses if you will.
Source Wassim
Same classic 45-degree pattern, dark version.
Source Luke McDonald
A seamless pattern the starting point for which was a 'colour modulo' texture in Paint.net.
Source Firkin
This background pattern contains a seamless texture of bark. It's not very realistic, but I think it looks quite nice.
Source V. Hartikainen
Number 4 in a series of 5 beautiful patterns. Can be found in colors on the submitter’s website.
Source Janos Koos
Gold Triangular Seamless Pattern No Background
Source GDJ
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Prismatic Curved Diamond Pattern 5 No Background
Source GDJ
Inspired by a drawing in 'Poems', James Smith, 1881.
Source Firkin
Geometric triangles seem to be quite hot these days.
Source Pixeden
A seamless web texture of "green stone".
Source V. Hartikainen
From a drawing in 'Resa i Afrika, genom Angola, Ovampo och Damaraland', P. Moller, 1899.
Source Firkin
An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
Old China with a modern twist, take two.
Source Adam Charlts