Update: Array comprehensions were removed from the standard. Quoting MDN:

The array comprehensions syntax is non-standard and removed starting with Firefox 58. For future-facing usages, consider using Array.prototype.map, Array.prototype.filter, arrow functions, and spread syntax.

See this answer for an example with Array.prototype.map:

let emails = people.map(({ email }) => email);

Original answer:

Yes, JavaScript will support array comprehensions in the upcoming EcmaScript version 7.

Here's an example.

var str =  "1234-5";
var ignore = "-";

console.log([for (i of str) if (!ignore.includes(i)) i]);

Given the question's Python code

print([int(i) for i in str(string) if i not in forbidden])

this is the most direct translation to JavaScript (ES2015):

const string = '1234-5';
const forbidden = '-';

console.log([...string].filter(c => !forbidden.includes(c)).map(c => parseInt(c)));
// result: [ 1, 2, 3, 4, 5 ]

Here is a comparison of the Python and JavaScript code elements being used: (Python -> Javascript):

• print -> console.log
• iterate over characters in a string -> spread operator
• list comprehension 'if' -> Array.filter
• list comprehension 'for' -> Array.map
• substr in str? -> string.includes

Reading the code, I assume forbidden can have more than 1 character. I'm also assuming the output should be "12345"

var string = "12=34-5";

var forbidden = "=-";

console.log(string.split("").filter(function(str){
    return forbidden.indexOf(str) < 0;
}).join(""))

If the output is "1" "2" "3" "4" "5" on separate lines

var string = "12=34-5";

var forbidden = "=-";

string.split("").forEach(function(str){
    if (forbidden.indexOf(str) < 0) {
        console.log(str);
    }
});