$('#apply-form input').blur(function()
{
    if( !$(this).val() ) {
          $(this).parents('p').addClass('warning');
    }
});

And you don’t necessarily need .length or see if it’s >0 since an empty string evaluates to false anyway but if you’d like to for readability purposes:

$('#apply-form input').blur(function()
{
    if( $(this).val().length === 0 ) {
        $(this).parents('p').addClass('warning');
    }
});

If you’re sure it will always operate on a textfield element then you can just use this.value.

$('#apply-form input').blur(function()
{
      if( !this.value ) {
            $(this).parents('p').addClass('warning');
      }
});

Also you should take note that $('input:text') grabs multiple elements, specify a context or use the this keyword if you just want a reference to a lone element (provided there’s one textfield in the context’s descendants/children).