Greiner-Hormann polygon clipping
 
- Does AND, OR, XOR (intersection, union, difference, if you're human)
 - Plays nicely with Leaflet, comes with an adaptor for it
 - Handles non-convex polygons and multiple clipping areas
 - ~3kb compressed, no dependencies
 
Note: If you are looking for something more powerful, take a look at the Martinez polygon clipping implementation.
Install
$ npm install greiner-hormann 
Browserify
var greinerHormann = require('greiner-hormann'); 
Browser
<script src="path/to/greiner-hormann(.leaflet).min.js"></script> 
Use
...
var intersection = greinerHormann.intersection(source, clip);
var union        = greinerHormann.union(source, clip);
var diff         = greinerHormann.diff(source, clip);
...
if(intersection){
    if(typeof intersection[0][0] === 'number'){ // single linear ring
        intersection = [intersection];
    }
    for(var i = 0, len = intersection.length; i < len; i++){
        L.polygon(intersection[i], {...}).addTo(map);
    }
} 
Format
Input and output can be {x:x, y:y} objects or [x,y] pairs. It will output the points in the same format you put in.