To get the tile this is based on select the rectangle in Inkscape and use shift+alt+i
Source Firkin
A dark pattern made out of 3×3 circles and a 1px shadow. This works well as a carbon texture or background.
Source Atle Mo
A seamless pattern of dark bricks. Maybe it's not very realistic, but it looks good in my opinion.
Source V. Hartikainen
A slightly grainy paper pattern with small horizontal and vertical strokes.
Source Atle Mo
A seamless pattern formed from a square tile. To get the tile, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
One more sharp little tile for you. Subtle circles this time.
Source Blunia
ZeroCC tileable stone texture, edited from pixabay. CC0
Source Sojan Janso
Background formed from the original with an emboss effect.
Source Firkin
Prismatic Curved Diamond Pattern 6 No Background
Source GDJ
Detailed but still subtle and quite original. Lovely gray shades.
Source Kim Ruddock
This was formed by distorting an image of a background on Pixabay.
Source Firkin
Derived from elements found in a floral ornament drawing on Pixabay.
Source Firkin
Greyscale version of a pattern that came out of playing with the 'light rays' plug-in for Paint.net
Source Firkin
Horizontal and vertical lines on a light gray background.
Source Adam Anlauf
This is so subtle you need to bring your magnifier!
Source Carlos Valdez
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
From a drawing in 'Uit de geschiedenis der Heilige Stede te Amsterdam', Yohannes Sterck, 1898.
Source Firkin
Prismatic Groovy Concentric Background 2 No Black
Source GDJ
Utilising some flowers from Almeidah. To get the unit tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
A bit simplified version. Although it could be edited out to be simpler. Anyway, this time the tiling is converted to a pattern fill -which is using clipping for the tile's edges.
Source Lazur URH
A seamless pattern the unit cell for which can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
A free seamless background texture that looks like a brown stone wall.
Source V. Hartikainen