Disable spaces in Input, AND allow back arrow?

This seems to work for me:

<input type="text" onkeypress="return event.charCode != 32">

You may add keydown handler and prevent default action for space key (i.e. 32):

$("input#UserName").on({
  keydown: function(e) {
    if (e.which === 32)
      return false;
  },
  change: function() {
    this.value = this.value.replace(/\s/g, "");
  }
});

DEMO: http://jsfiddle.net/EJFbt/1/

It doesn't "disable" the back arrow — your code keeps replacing all the text outright, whenever you press a key, and every time that happens the caret position is lost.

Simply don't do that.

Use a better mechanism for banning spaces, such as returning false from an onkeydown handler when the key pressed is space:

$(function() {
    $("input#Username").on("keydown", function (e) {
        return e.which !== 32;
    });​​​​​
});

This way, your textbox is prohibited from receiving the spaces in the first place and you don't need to replace any text. The caret will thus remain unaffected.

---

Update

@VisioN's adapted code will also add this space-banning support to copy-paste operations, whilst still avoiding text-replacement-on-keyup handlers that affect your textbox value whilst your caret is still active within it.

So here's the final code:

$(function() {

    // "Ban" spaces in username field
    $("input#Username").on({

       // When a new character was typed in
       keydown: function(e) {

          // 32 - ASCII for Space;
          // `return false` cancels the keypress
          if (e.which === 32)
             return false;
       },

       // When spaces managed to "sneak in" via copy/paste
       change: function() {
          // Regex-remove all spaces in the final value
          this.value = this.value.replace(/\s/g, "");
       }

       // Notice: value replacement only in events
       //  that already involve the textbox losing
       //  losing focus, else caret position gets
       //  mangled.
    });​​​​​
});