The YUI Compressor and dojo shrinksafe should work perfectly fine without semicolons since they're based on a full javascriptJavaScript parser. But Packer and JSMin won't.
The other reason to always use semi-colons at the end of statements is that occasionally you can accidentally combine two statements to create something very different. For example, if you follow the statement with the common technique to create a scope using a closure:
var literal = {
say: function(msg) { alert(msg); }
}
(function() {
// ....
})();
The parser might interpret the brackets as a function call, here causing a type error, but in other circumstances it could cause a subtle bug that's tricky to trace. Another interesting mishap is if the next statement starts with a regular expression, the parser might think the first forward slash is a division symbol.