Sort of like the Photoshop transparent background, but better!
Source Alex Parker
Love me some light mesh on a Monday. Sharp.
Source Wilmotte Bastien
A pattern formed from a photograph of a 16th century ceramic tile.
Source Firkin
This is lovely, just the right amount of subtle noise, lines and textures.
Source Richard Tabor
Just the symbols of the signs of the zodiac distributed in a chequer board-like pattern
Source Firkin
A seamless background texture of old cardboard.
Source V. Hartikainen
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
From a drawing in 'From Snowdon to the Sea. Striking stories of North and South Wales', Marie Trevelyan, 1895.
Source Firkin
Retro Circles Background 7 No Black
Source GDJ
Beautiful dark noise pattern with some dust and grunge.
Source Vincent Klaiber
A seamless texture traced from an image on opengameart.org shared by Scouser.
Source Firkin
Remixed from a drawing in 'Chambéry à la fin du XIVe siècle', Timoleon Chapperon, 1863.
Source Firkin
Seamless Prismatic Pythagorean Line Art Pattern No Background. A seamless pattern that includes the original tile (go to Objects / Pattern / Pattern To Objects in Inkscape's menu to extract it).
Source GDJ
Here's a camo print with more tan and less green, such as might be used in a desert scenario. This is tileable, so it can be used as a wallpaper or background.
Source Eady
Drawn in Paint.net and vectorised in Vector Magic.
Source Firkin
A set of paper filters. The base texture is generated the same way, only the compositing mode is varied.
Source Lazur URH
A grid of squares with green colours. Since the colours are randomly distributed it is automatically seamless.
Source Firkin
A simple bump filter made upon request at irc #inkscape at freenode. Made a screen capture of the making here: https://youtu.be/TGAWYKVLxQw
Source Lazur URH