Does jQuery validation plugin have some dependencies? For example, I saw blogposts that said delegate plugin should be used... but I don't see this plugin reference at any validation plugin example (for example, here: http://jquery.bassistance.de/validate/demo/milk/).
The question arouse because validation plugin doesn't catch submit at my application.
Its only dependency is jQuery - check out the source code for the Remember the Milk example page linked in your question. It includes 4 references to .js files:
<script src="../../lib/jquery.js" type="text/javascript"></script>
<script src="../../jquery.validate.js" type="text/javascript"></script>
...
<script src="http://www.google-analytics.com/urchin.js" type="text/javascript">
</script>
...
<script src="../js/chili-1.7.pack.js" type="text/javascript"></script>
The first two are the required ones for jQuery validate - the third is google analytics tracking (unrelated to jQuery Validate), and the last one is code highlighting (also unrelated to jQuery Validate)
There's probably a problem with the configuration to the plugin in your application - perhaps post another question with some details about that.