An abstract texture of water. It's not perfect, but will do. You may download if you like it.
Source V. Hartikainen
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
Remixed from a design seen in 'Burghley. The Life of William Cecil', William Charlton, 1857
Source Firkin
Love the style on this one, very fresh. Diagonal diamond pattern. Get it?
Source INS
Prismatic Rounded Squares Grid 3 No Background
Source GDJ
Prismatic Isometric Cube Extra Pattern No Background
Source GDJ
Heavy depth and shadows here, but might work well on some mobile apps.
Source Damian Rivas
Dead simple but beautiful horizontal line pattern.
Source Fabian Schultz
To get the tile this is based on, select the rectangle in Inkscape and use shift+alt+i.
Source Firkin
From a drawing in 'Gately's World's Progress', Charles Beale, 1886.
Source Firkin
A background formed from an image of an old tile on the New York Metropolitan Museum of Art website. To get the base tile, select the rectangle in Inkscape and use shift-alt-i.
Source Firkin
Very dark pattern with some noise and 45-degree lines.
Source Stefan Aleksić
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
A repeating background of beige paper with vintage look. Repeats to infinity, as usual.
Source V. Hartikainen
Prismatic Geometric Tessellation Pattern 4 No Background
Source GDJ
A version without colours blended together to give a different look.
Source Firkin
ZeroCC tileable stone texture, edited from pixabay. CC0
Source Sojan Janso
This is lovely, just the right amount of subtle noise, lines and textures.
Source Richard Tabor