From a drawing in 'At home', J. Sowerby, J. Crane and T. Frederick, 1881.
Source Firkin
Vertical lines with a bumpy, yet crisp, feel to it.
Source Raasa
Remixed from a drawing in 'Some account of the Worshipful Company of Ironmongers', John Nicholl, 1866.
Source Firkin
Sort of like the Photoshop transparent background, but better!
Source Alex Parker
A pattern formed from a squared tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i.
Source Firkin
Dare I call this a «flat pattern»? Probably not.
Source Dax Kieran
From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.
Source Firkin
Light square grid pattern, great for a “DIY projects” sort of website, maybe?
Source Rafael Almeida
A dark metallic background with a pattern of stamped dots. Here's a dark "metallic" background pattern for you.
Source V. Hartikainen
You guessed it – looks a bit like cloth.
Source Peax Webdesign
One more from Badhon, sharp horizontal lines making an embossed paper feeling.
Source Badhon Ebrahim
Clover with background for St. Patrick's Day. Add to a card with a doily, ribbon, a leprechaun or other embellishments.
Source BAJ
A set of paper filters. The base texture is generated the same way, only the compositing mode is varied.
Source Lazur URH
Based on several public domain drawings on Wikimedia Commons. This was formed from a rectangular tile. The tile can be accessed in Inkscape by selecting the rectangle and using shift-alt-i
Source Firkin
Prismatic Groovy Concentric Background 2
Source GDJ
This one resembles a black concrete wall when is tiled. It should look great, at least with dark website themes.
Source V. Hartikainen