Chinese dictionaries have organized their thousands of characters with the radical system for the last few hundred years. In this visualization we lay out all 214 standard radicals. Clicking on one will rapidly overlay all the characters with that radical.
This visualization is only showing characters from the about ~2500 simplified characters, so not all radicals have a set of characters to visualize.
You may notice some radicals look more complicated than the rendered characters, this is because the radical is being shown in its traditional variation while the characters are all simplified.
There is a similar visualization of the traditional characters here
An excellent example of looking up Chinese characters by their radical: http://hanzi.hemiola.com/