closure_alternatives.js

////////////////////////////
// using inline closure
////////////////////////////
(function() {  
  arr = []
  
  for (i = 0; i < 10; i++)
    arr[i] = (function(i) {
      return function() { console.log("I am #" + i) }
    })(i)
  
  for (j = 0; j < 10; j++)
    arr[j]()
})()

/////////////////////////////////
// using closure in a function
/////////////////////////////////
(function() {  
  arr = []
  
  function closure(i, fn) {
    return function() { return fn(i) }
  }
    
  for (i = 0; i < 10; i++)
    arr[i] = closure(i, function(i) { console.log("I am #" + i) })
    
  for (j = 0; j < 10; j++)
    arr[j]()
})()

//////////////////////////////
// using Function constructor
//////////////////////////////
(function() {
  arr = []
  
  for (i = 0; i < 10; i++)
    arr[i] = Function("console.log('I am #" + i + "')")
    
  for (j = 0; j < 10; j++)
    arr[j]()
})()

/////////////////////////////
// using bind 
/////////////////////////////
(function() {
  arr = []
  
  for (i = 0; i < 10; i++)
    arr[i] = function(i) { console.log("I am #" + i) }.bind(null, i)
    
  for (j = 0; j < 10; j++)
    arr[j]()
})()

//////////////////////////////
// using let (requires ES6)
//////////////////////////////
// In Chrome (v46) ! I have to use strict mode to use "let" 
//  ~ which also does not allow globals
//  ~ so we must add var in front of variable names
(function() {
  'use strict'
  var arr = []
  
  for (let i = 0; i < 10; i++) 
    arr[i] = function() { console.log("I am #" + i) }
    
  for (var j = 0; j < 10; j++) 
    arr[j]()
})()

////////////////////////
// using currying
////////////////////////
(function() {  
  arr = []
  function curry(i) { 
    return function(fn) { 
      return function() { 
        return fn(i) 
      } 
    } 
  }
  
  for (i = 0; i < 10; i++) 
    arr[i] = curry(i)(function(i) { console.log("I am #" + i) })
    
  for (j = 0; j < 10; j++) 
    arr[j]()
})()

/////////////////////////
// using Array functions
/////////////////////////
(function() {  
  arr = Array(10)
  arr.fill(null)
     .forEach(function(_, i) { 
       arr[i] = function() { console.log("I am #" + i) }
     })
     
  for (j = 0; j < 10; j++) 
    arr[j]()
})()

/////////////////////////////
// using time indexing array
/////////////////////////////
(function() {  
  arr = []
  t = [] // time index -- stores a value at each loop interation
  
  for (i = 0; i < 10; i++) {
    t[i] = i // you could record any value for this time point
    arr[i] = function(i) { console.log("I am #" + i) }
  }
  
  for (j = 0; j < 10; j++)
    arr[j](t[j]) // Note: this function invocation is different than other alternatives
})()

http://jsperf.com/closure-alternativess

Each of the alternatives here are made to be copy/pasted directly into your javascript console. You will instantly see the results.
The jsperf link above has versions of each of these with just the "setting values" portion.

Added two more alternatives: http://jsperf.com/closure-alternativess/4