If I'm cooking 
anything savory, it will start with some kind of onions.
As a garnish? Always raw. Tacos, pho, tempura, hot dogs, whatever: raw onions help (all hot dogs should have mustard and raw onion, at a minimum).
Never rinsed, except to get dirt off of them, and that's either before they touch any slicing implement, or, if not so fresh, just after a slice to take off the mushy outer layer. Never rinse after they've been cut up.
Raw onions a good addition to short pickles, too.
And, of course, you should listen to a rendition of Green Onions, while you slice onions.
	
		
	
	
		
		
			I'd rather lose an arm then have to never eat onions again.
		
		
	 
On this, I can agree w/ Spidey07.