There are at least five ways. The best option, which should also be the fastest (owing to the native RegEx engine) is placed at the top.
Method 1
("this is foo bar".match(/o/g)||[]).length;
// returns 2
Method 2
"this is foo bar".split("o").length - 1;
// returns 2
Split not recommended as it is resource hungry. It allocates new instances of 'Array' for each match. Don't try it for a >100MB file via FileReader. You can observe the exact resource usage using Chrome's profiler option.
Method 3
var stringsearch = "o"
,str = "this is foo bar";
for(var count=-1,index=-2; index != -1; count++,index=str.indexOf(stringsearch,index+1) );
// returns 2
Method 4
Searching for a single character
var stringsearch = "o"
,str = "this is foo bar";
for(var i=count=0; i<str.length; count+=+(stringsearch===str[i++]));
// returns 2
Method 5
Element mapping and filtering. This is not recommended due to its overall resource preallocation rather than using Pythonian 'generators':
var str = "this is foo bar"
str.split('').map( function(e,i){ if(e === 'o') return i;} )
.filter(Boolean)
//>[9, 10]
[9, 10].length
// returns 2
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I made this gist, with currently 8 methods of character-counting, so we can directly pool and share our ideas - just for fun, and perhaps some interesting benchmarks :)