My friends and I have observed that the act of using a flash in informal settings (for example, pictures of a Christmas party or a busy toddler) tends to draw attention to the photographer and thus disrupt the scene we were trying to capture. Because of this, I tend to avoid the flash (external or on-camera) and just try to get the most light I can. But these are exactly the sort of poorly lit, dynamic situations that you'd want a flash for! How do I resolve this Heisenberg-ian paradox?
(Edit: When I said "off-camera", I really meant "not the built-in flash", I have a Canon Speedlite 430EX 2. Thank you for answers which cover both of the types!)