Transparent Square Tiles@2X #299
 Grid  CC BY-SA 3.0

The first pattern on here using opacity. Try it on a site with a colored background, or even using mixed colors.

Source Nathan Spady

 More Textures
Graphy@2X #351
 Grid  CC BY-SA 3.0

Looks like a technical drawing board: small squares forming a nice grid.

Source We Are Pixel8

Background pattern 259 #2133
 Red  CC 0

Remixed from a design seen on Pixabay. The basic tile can be had by selecting the rectangle in Inkscape and using shift+alt+i.

Source Firkin

Diamond pattern 2 (colour 2) #2267
 Colorful  CC 0

From a tile that can be had by selecting the rectangle in Inkscape and using shift+alt+i.

Source Firkin

Decorative divider 217 #2233
 Dark  CC 0

Remixed from a drawing in 'Maidenhood; or, the Verge of the Stream', Laura Jewry, 1876.

Source Firkin

Prismatic Dots Background 5@2X #510
 Noise  CC 0

Prismatic Dots Background 5

Source GDJ

Project Papper@2X #120
 Paper  CC BY-SA 3.0

Light square grid pattern, great for a “DIY projects” sort of website, maybe?

Source Rafael Almeida

Prismatic Geometric Pattern Variation 2 With Background@2X #472
 Noise  CC 0

Prismatic Geometric Pattern Variation 2 With Background

Source GDJ

Medic Packaging Foil@2X #377
 Light  CC BY-SA 3.0

8 by 8 pixels, and just what the title says.

Source pixilated

Decorative divider 274 #1922
 Dark  CC 0

Redrawn based on a drawing in 'По Сѣверо-Западу Россіи' Konstantin Sluchevsky, 1897.

Source Firkin

Handmade Paper #37
 Paper  CC BY-SA 3.0

White handmade paper pattern with small bumps.

Source Marquis

Paven #296
 Grid  CC BY-SA 3.0

A subtle shadowed checkered pattern. Increase the lightness for even more subtle sexiness.

Source Josh Green

Decorative divider 228 #2154
 Dark  CC 0

Remixed from a design found in 'History of the Virginia Company of London; with letters to and from the first Colony, never before printed', Edward Neill, 1869.

Source Firkin