How to keep flash from disrupting the scene?

Question

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!)

Answer

1. Bounce flash is much better, since it's less directly (and literally) in-your-face.
2. Off-camera bounce flash is even better. If you're using a wireless radio system, that's probably best of all, but I actually have pretty good results using my camera's built-in optical TTL wireless (I suppose since it's less powerful than a full flash burst), particularly when combined with:
3. Start shooting early and do it often; people will get used to it and start ignoring you.

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