Here's a repeatable texture that resembles a light green concrete wall or something similar.
Source V. Hartikainen
From a drawing in 'Artists and Arabs', Henry Blackburn, 1868
Source Firkin
Drawn in Paint.net using the kaleidoscope plug-in and vectorised.
Source Firkin
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
A seamless pattern the starting point for which was a 'rainbow twist' texture in Paint.net.
Source Firkin
From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Alternative colour scheme. 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
A seamless design of flowers remixed from a jpg on Pixabay by Prawny.
Source Firkin
This light blue background pattern is quite pleasing to the eye, it consists of a tiny rough grid pattern, which is seamless by design. That's it, if you like the color, you can use this seamless pattern in a web design without making any further modifications to it.
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
A seamless pattern based on a square tile that can be retrieved in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Just to prove my point, here is a slightly modified dark version.
Source Atle Mo
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
A nice and simple gray stucco material. Great on its own, or as a base for a new pattern.
Source Bartosz Kaszubowski
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
From a drawing in 'A Guide to the Guildhall of the City of London', John Baddeley, 1898.
Source Firkin
From a drawing in 'Less Black than we're painted', James Payn, 1884.
Source Firkin