When to dip into the Emergecy Fund?

When is an emergency, really an emergency? I'm talking about when is it justifiable to use money inside of an Emergency Fund. I feel so darn guilty even thinking of having to use it in the New Year that I guess that's a good thing, at least I don't dip into it mindlessly - but still, when is it okay to do so? I know this will vary from person to person based on different situations, but what have been your experiences? I'm afraid that once we touch ours, we will never be able to rebuild it. I think this is why I really want to get our Line of Credit paid down as much as possible. It's not been a priority for us, because we keep current with our payments on it, the interest rate is really low and it's life and disability insured. By paying down the Line of Credit faster than we had previously expected, we will then free up extra money through the monthly budget. We still have a ways to go in paying it off, but the balance owing is decreasing, and that is always a good thing, because come the New Year and depending on hubby's work situation, we might not be able to throw extra onto it, so it's best to do whatever we can now.

Hubby has been able to get some overtime hours on Tuesday and Wednesday and hoping for some more tonight, as the merge between the 2 warehouses are now taking place. The new company is allowing over time for the next 2 weeks only. We are taking advantage of this, to make as much money as possible, so that we can bank the money.