UPDATE January, 2017:

According to Can I use, the user-select is currently supported in all browsers except Internet Explorer 9 and earlier versions (but sadly still needs a vendor prefix).


All of the correct CSS variations are:

.noselect {
  -webkit-touch-callout: none; /* iOS Safari */
    -webkit-user-select: none; /* Safari */
     -khtml-user-select: none; /* Konqueror HTML */
       -moz-user-select: none; /* Old versions of Firefox */
        -ms-user-select: none; /* Internet Explorer/Edge */
            user-select: none; /* Non-prefixed version, currently
                                  supported by Chrome, Edge, Opera and Firefox */
}

<p>
  Selectable text.
</p>
<p class="noselect">
  Unselectable text.
</p>

Note that user-select is in standardization process (currently in a W3C working draft). It is not guaranteed to work everywhere, and there might be differences in implementation among browsers and in the future browsers can drop support for it.


More information can be found in Mozilla Developer Network documentation.