A seamless gray background texture suitable for use on websites. To me, it has the look of stone. Feel free to modify it to meet your needs (by making it a bit lighter or darker, for example).
Source V. Hartikainen
A beautiful dark wood pattern, superbly tiled.
Source Omar Alvarado
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
More Japanese-inspired patterns, Gold Scales this time.
Source Josh Green
Zero CC Mossy stone tileable texture, photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
This one is amazing, truly original. Go use it!
Source Viahorizon
This is the third pattern called Dark Denim, but hey, we all love them!
Source Brandon Jacoby
Geometric triangles seem to be quite hot these days.
Source Pixeden
Did anyone say The Hoff? This pattern is in no way related to Baywatch.
Source Josh Green
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
From a drawing in 'Hundert Jahre in Wort und Bild', S. Stefan, 1899.
Source Firkin
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
Not a pattern for fabrics, but one produced from a jpg of a stack of fabric items that was posted on Pixabay. The tile that this is based on can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Farmer could be some sort of fabric pattern, with a hint of green.
Source Fabian Schultz
Sweet and subtle white plaster with hints of noise and grunge.
Source Phil Maurer
Zerro CC tillable texture of stones photographed and made by me. CC0
Source Sojan Janso