How to Escape Only Single Quotes

How do I escape only single quotes?

Quite simply: echo str_replace('\'', '\\\'', $myString);
However, I'd suggest use of JSON and json_encode() function as it will be more reliable (quotes new lines for instance):

<?php $data = array('myString' => '...'); ?>

<script>
   var phpData = <?php echo json_encode($data) ?>;
   alert(phpData.myString);
</script>

How to escape single quotes within single quoted strings

If you really want to use single quotes in the outermost layer, remember that you can glue both kinds of quotation. Example:

 alias rxvt='urxvt -fg '"'"'#111111'"'"' -bg '"'"'#111111'"'"
 #                     ^^^^^       ^^^^^     ^^^^^       ^^^^
 #                     12345       12345     12345       1234

Explanation of how '"'"' is interpreted as just ':

' End first quotation which uses single quotes.
" Start second quotation, using double-quotes.
' Quoted character.
" End second quotation, using double-quotes.
' Start third quotation, using single quotes.

If you do not place any whitespaces between (1) and (2), or between (4) and (5), the shell will interpret that string as a one long word.

How to escape the single quotes and double quotes at the same time

Use a backslash character (\) to escape it:

$("#divId").html('<div onclick="location.href=\"xxx\""');

Here are characters that need to be escaped in javascript strings:

Horizontal Tab: \t
Vertical Tab: \v
Nul char: \0
Backspace: \b
Form feed: \f
Newline: \n
Carriage return: \r
Single quote: \'
Double quote: \"
Backslash: \\

As stated in the comments, I would do something different in this case:

$('#divId').html('<div id="foo">');
$('#foo').click(function() {
    window.location.href = 'xxx';
});

Escape only single quotes (leave double quotes alone) with htmlspecialchars()

str_replace("'", "\\'", $string);

There.

Or, use ENT_QUOTES

htmlspecialchars($string, ENT_QUOTES);

How do I escape a single quote in SQL Server?

Single quotes are escaped by doubling them up, just as you've shown us in your example. The following SQL illustrates this functionality. I tested it on SQL Server 2008:

DECLARE @my_table TABLE (
    [value] VARCHAR(200)
)

INSERT INTO @my_table VALUES ('hi, my name''s tim.')

SELECT * FROM @my_table

Results

value
==================
hi, my name's tim.

How do I escape a single quote ( ' ) in JavaScript?

You should always consider what the browser will see by the end. In this case, it will see this:

<img src='something' onmouseover='change(' ex1')' />

In other words, the "onmouseover" attribute is just change(, and there's another "attribute" called ex1')' with no value.

The truth is, HTML does not use \ for an escape character. But it does recognise " and ' as escaped quote and apostrophe, respectively.

Armed with this knowledge, use this:

document.getElementById("something").innerHTML = "<img src='something' onmouseover='change("ex1")' />";

... That being said, you could just use JavaScript quotes:

document.getElementById("something").innerHTML = "<img src='something' onmouseover='change(\"ex1\")' />";

Escaping single quotes in JavaScript string for JavaScript evaluation

The thing is that .replace() does not modify the string itself, so you should write something like:

strInputString = strInputString.replace(...

It also seems like you're not doing character escaping correctly. The following worked for me:

strInputString = strInputString.replace(/'/g, "\\'");