When is it a good idea to let an academic department (or a professor) know that I have Asperger's (or ADD)? With Asperger's, the trick is always when to explain it (in a non-awkward situation). I'd like to avoid mentioning it if possible, but it has gotten to the point that I only mention it after committing a major social faux pas, in which case it might be seen as an excuse.

With ADD, this is an issue that happens when people explain things to me. I often don't parse things very well when they're communicated to me verbally since I do have attention lapses. That's the major issue, anyways. 

With that said, I do (indirectly) imply that I have both diagnoses on my personal website.
I agree with aeismail's answer, however I would just add that you might need be careful about the perception of your condition(s), especially the negative aspects. For instance, with the ADD, it's better to ask people to send written copies because you have a visual memory, because it's a constructive remark, rather than saying that you don't fully understand verbal explanation. Myself, I ask people to send emails about important things, and I clearly state that it's due to my great visual memory and my terrible auditive memory. 

In other words, I think it's a good idea to inform people that you have Asperger or ADD, especially those you work closely with, but it's more important to explain the positive aspects rather than just stating your condition.