Geometric triangles seem to be quite hot these days.
Source Pixeden
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Some rectangles, a bit of dust and grunge, plus a hint of concrete.
Source Atle Mo
Adapted from an image that was uploaded to Pixabay by Anerma.
Source Firkin
A very dark spotted twinkle pattern for your twinkle needs.
Source Badhon Ebrahim
A pale yellow background pattern with vertical stripes. The stripes are partially faded. I think this background image turned out pretty well, especially those faded stripes.
Source V. Hartikainen
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Inspired by a 1930s wallpaper pattern I saw on TV.
Source Firkin
This background texture resembles stone. It may be used as a background on web pages or on some of their html elements (header, borders, menu bar, etc.). Just modify it for your needs.
Source V. Hartikainen
From a drawing in 'Art Embroidery', M.S. Lockwood and E. Glaister, 1878.
Source Firkin
The tile this is based on can be retrieved by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
This one is super crisp at 2X. Lined paper with some dust and scratches.
Source HQvectors
Zero CC tileable seed texture, edited by me to be seamless from a Pixabay image. CC0
Source Sojan Janso
Simple gray checkered lines, in light tones.
Source Radosław Rzepecki
Seamless pattern the tile for which can be had by using shift-alt-I on the selected rectangle in Inkscape.
Source Firkin
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
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
Fabric-ish patterns are close to my heart. French Stucco to the rescue.
Source Christopher Buecheler
If you want png files of this u can download them here : viscious-speed.deviantart.com/gallery/27635117
Source Viscious-Speed
This seamless background image should look nice on websites. It has a dark blue gray texture with vertical stripes, it tiles seamlessly and, like all of the background images here, it's free. So, if you like it, take it!
Source V. Hartikainen