Checkered Light Emboss #280
 Grid  CC BY-SA 3.0

Sort of like the Photoshop transparent background, but better!

Source Alex Parker

 More Textures
Prismatic Groovy Concentric Background 5 No Black@2X #468
 Dark  CC 0

Prismatic Groovy Concentric Background 5 No Black

Source GDJ

Colourful background #2011
 Colorful  CC 0

Made by distorting a simple pattern using the 'sin waves' plugin for Paint.net and vectorising in Vector Magic

Source Firkin

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

Colorful Bicycles Background #207
 Noise  CC 0

Pixabay.

Source GDJ

Prismatic Abstract Line Art Pattern Background@2X #566
 Dark  CC 0

Prismatic Abstract Line Art Pattern Background

Source GDJ

Background pattern 328 (colour 6) #1796
 Red  CC 0

To get the tile this is based on select the rectangle in Inkscape and use shift-alt-i

Source Firkin

Interlocking pattern 3 #2406
 Grid  CC 0

A seamless pattern formed from a square tile. The tile can be retrieved by selecting the rectangle in Inkscape and using shift-alt-I.

Source Firkin

Background pattern 227 #2314
 Yellow  CC 0

A seamless background drawn in Paint.net and vectorised with Vector Magic. The starting point was a photograph of drinking straws from Pixabay.

Source Firkin