CSS
CSS 3 has a blur filter (only webkit at the moment Nov 2014):
-webkit-filter: blur(3px); /*chrome (android), safari (ios), opera*/
IE 4-9 supports a non-standard filter
filter:progid:DXImageTransform.Microsoft.Blur(PixelRadius='3')
See some nice demo for the blur and other filters here.
For future reference here is the compatibility table for CSS filter. Firefox seems to be getting the feature in v35+ while even IE11 does not seem to have any compatibility.
SVG
An alternative is using svg (safe for basically IE9 and up):
filter: url(blur.svg#blur);
SVG:
<svg version="1.1" xmlns="http://www.w3.org/2000/svg">
<filter id="blur">
<feGaussianBlur stdDeviation="3" />
</filter>
</svg>
Javascript
You will achieve the highest browser compatibility with javascript, but usually the slowest performance and added complexity to your js.
- http://www.blurjs.com/ (jquery plugin, canvas solution so IE9+, FF, Chrome support)
- http://nbartlomiej.github.io/foggy/ (jquery plugin IE8+, FF,Chrome support)