Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
To get the tile this is based on, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A free seamless background image with abstract texture of green "curtain".
Source V. Hartikainen
A heavy hitter at 400x400px, but lovely still.
Source Breezi
Like the name says, light and gray, with some small dots and circles.
Source Brenda Lay
From a drawing in 'The Quiver of Love', Walter Crane, 1876
Source Firkin
A repeating background of beige paper with vintage look. Repeats to infinity, as usual.
Source V. Hartikainen
A seamless design of flowers remixed from a jpg on Pixabay by Prawny.
Source Firkin
Some more diagonal lines and noise, because you know you want it.
Source Atle Mo
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
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
"Beige Stone", Tileable Texture.
Source V. Hartikainen
Prismatic Groovy Concentric Background No Black
Source GDJ
One week and it's Easter already. Thought I would revisit the decorated egg contest at inkscape community: http://forum.inkscapecommunity.com/index.php?topic=118.0
Source Lazur URH
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
From a drawing in 'Les Chroniqueurs de l'Histoire de France depuis les origines jusqu'au XVIe siècle', Henriette Witt, 1884.
Source Firkin
Redrawn based on a drawing in 'По Сѣверо-Западу Россіи' Konstantin Sluchevsky, 1897.
Source Firkin
Prismatic Curved Diamond Pattern 3 No Background
Source GDJ
A seamless pattern from a tile drawn in Paint.net and vectorised in Vector Magic
Source Firkin